MAA Rocky Mountain Section Meeting
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BERNOULLI NEWS, Vol 24 No 1 (2017)
Vol. 24 (1), May 2017 Published twice per year by the Bernoulli Society ISSN 1360–6727 CONTENTS News from the Bernoulli Society p. 1 Awards and Prizes p. 2 New Executive Members A VIEW FROM THE PRESIDENT in the Bernoulli Society Dear Members of the Bernoulli Society, p. 3 As we all seem to agree, the role and image of statistics has changed dramatically. Still, it takes ones breath when realizing the huge challenges ahead. Articles and Letters Statistics has not always been considered as being very necessary. In 1848 the Dutch On Bayesian Measures of Ministry of Home Affairs established an ofŮice of statistics. And then, thirty years later Uncertainty in Large or InŮinite minister Kappeyne van de Coppelo abolishes the “superŮluous” ofŮice. The ofŮice was Dimensional Models p. 4 quite rightly put back in place in 1899, as “Centraal Bureau voor de Statistiek” (CBS). Statistics at the CBS has evolved from “simple” counting to an art requiring a broad range On the Probability of Co-primality of competences. Of course counting remains important. For example the CBS reports in of two Natural Numbers Chosen February 2017 that almost 1 out of 4 people entitled to vote in the Netherlands is over the at Random p. 7 age of 65. But clearly, knowing this generates questions. What is the inŮluence of this on the outcome of the elections? This calls for more data. Demographic data are combined with survey data and nowadays also with data from other sources, in part to release the “survey pressure” that Ůirms and individuals are facing. -
The Many Faces of Alternating-Sign Matrices
The many faces of alternating-sign matrices James Propp Department of Mathematics University of Wisconsin – Madison, Wisconsin, USA [email protected] August 15, 2002 Abstract I give a survey of different combinatorial forms of alternating-sign ma- trices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, three- colorings, monotone triangles, tetrahedral order ideals, square ice, gasket- and-basket tilings and full packings of loops. (This article has been pub- lished in a conference edition of the journal Discrete Mathematics and Theo- retical Computer Science, entitled “Discrete Models: Combinatorics, Com- putation, and Geometry,” edited by R. Cori, J. Mazoyer, M. Morvan, and R. Mosseri, and published in July 2001 in cooperation with le Maison de l’Informatique et des Mathematiques´ Discretes,` Paris, France: ISSN 1365- 8050, http://dmtcs.lori.fr.) 1 Introduction An alternating-sign matrix of order n is an n-by-n array of 0’s, 1’s and 1’s with the property that in each row and each column, the non-zero entries alter- nate in sign, beginning and ending with a 1. For example, Figure 1 shows an Supported by grants from the National Science Foundation and the National Security Agency. 1 alternating-sign matrix (ASM for short) of order 4. 0 100 1 1 10 0001 0 100 Figure 1: An alternating-sign matrix of order 4. Figure 2 exhibits all seven of the ASMs of order 3. 001 001 0 10 0 10 0 10 100 001 1 1 1 100 0 10 100 0 10 0 10 100 100 100 001 0 10 001 0 10 001 Figure 2: The seven alternating-sign matrices of order 3. -
The Many Faces of Alternating-Sign Matrices
The many faces of alternating-sign matrices James Propp∗ Department of Mathematics University of Wisconsin – Madison, Wisconsin, USA [email protected] June 1, 2018 Abstract I give a survey of different combinatorial forms of alternating-sign ma- trices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, three- colorings, monotone triangles, tetrahedral order ideals, square ice, gasket- and-basket tilings and full packings of loops. (This article has been pub- lished in a conference edition of the journal Discrete Mathematics and Theo- retical Computer Science, entitled “Discrete Models: Combinatorics, Com- putation, and Geometry,” edited by R. Cori, J. Mazoyer, M. Morvan, and R. Mosseri, and published in July 2001 in cooperation with le Maison de l’Informatique et des Math´ematiques Discr`etes, Paris, France: ISSN 1365- 8050, http://dmtcs.lori.fr.) 1 Introduction arXiv:math/0208125v1 [math.CO] 15 Aug 2002 An alternating-sign matrix of order n is an n-by-n array of 0’s, +1’s and −1’s with the property that in each row and each column, the non-zero entries alter- nate in sign, beginning and ending with a +1. For example, Figure 1 shows an ∗Supported by grants from the National Science Foundation and the National Security Agency. 1 alternating-sign matrix (ASM for short) of order 4. 0 +1 0 0 +1 −1 +1 0 0 0 0 +1 0 +1 0 0 Figure 1: An alternating-sign matrix of order 4. Figure 2 exhibits all seven of the ASMs of order 3. -
Contemporary Mathematics 78
CONTEMPORARY MATHEMATICS 78 Braids Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group held July 13-26. 1986 at the University of California, Santa Cruz, California Joan S. Birman Anatoly Libgober Editors http://dx.doi.org/10.1090/conm/078 Recent Titles in This Series 120 Robert S. Doran, Editor, Selfadjoint and nonselfadjoint operator algebras and operator theory, 1991 119 Robert A. Melter, Azriel Rosenfeld, and Prabir Bhattacharya, Editors, Vision geometry, 1991 118 Yan Shi-Jian, Wang Jiagang, and Yang Chung-chun, Editors, Probability theory and its applications in China, 1991 117 Morton Brown, Editor, Continuum theory and dynamical systems, 1991 116 Brian Harboume and Robert Speiser, Editors, Algebraic geometry: Sundance 1988, 1991 115 Nancy Flournoy an'il Robert K. Tsutakawa, Editors, Statistical multiple integration, 1991 114 Jeffrey C. Lagarias and Michael J. Todd, Editors, Mathematical developments arising from linear programming, 1990 113 Eric Grinberg and Eric Todd Quinto, Editors, Integral geometry and tomography, 1990 112 Philip J. Brown and Wayne A. Fuller, Editors, Statistical analysis of measurement error models and applications, 1990 Ill Earl S. Kramer and Spyros S. Magliveras, Editors, Finite geometries and combinatorial designs, I 990 II 0 Georgia Benkart and J. Marshall Osborn, Editors, Lie algebras and related topics, 1990 109 Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang, Editors, Combinatorial group theory, 1990 108 Melvyn S. Berger, Editor, Mathematics of nonlinear science, 1990 107 Mario Milman and Tomas Schonbek, Editors, Harmonic analysis and partial differential equations, 1990 I 06 Wilfried Sieg, Editor, Logic and computation, 1990 I 05 Jerome Kaminker, Editor, Geometric and topological invariants of elliptic operators, 1990 I 04 Michael Makkai and Robert Pare, Accessible categories: The foundations of categorical model theory, 1989 I 03 Steve Fisk, Coloring theories, 1989 I 02 Stephen McAdam, Primes associated to an ideal, 1989 101 S.-Y. -
Alternating Sign Matrices and Polynomiography
Alternating Sign Matrices and Polynomiography Bahman Kalantari Department of Computer Science Rutgers University, USA [email protected] Submitted: Apr 10, 2011; Accepted: Oct 15, 2011; Published: Oct 31, 2011 Mathematics Subject Classifications: 00A66, 15B35, 15B51, 30C15 Dedicated to Doron Zeilberger on the occasion of his sixtieth birthday Abstract To each permutation matrix we associate a complex permutation polynomial with roots at lattice points corresponding to the position of the ones. More generally, to an alternating sign matrix (ASM) we associate a complex alternating sign polynomial. On the one hand visualization of these polynomials through polynomiography, in a combinatorial fashion, provides for a rich source of algo- rithmic art-making, interdisciplinary teaching, and even leads to games. On the other hand, this combines a variety of concepts such as symmetry, counting and combinatorics, iteration functions and dynamical systems, giving rise to a source of research topics. More generally, we assign classes of polynomials to matrices in the Birkhoff and ASM polytopes. From the characterization of vertices of these polytopes, and by proving a symmetry-preserving property, we argue that polynomiography of ASMs form building blocks for approximate polynomiography for polynomials corresponding to any given member of these polytopes. To this end we offer an algorithm to express any member of the ASM polytope as a convex of combination of ASMs. In particular, we can give exact or approximate polynomiography for any Latin Square or Sudoku solution. We exhibit some images. Keywords: Alternating Sign Matrices, Polynomial Roots, Newton’s Method, Voronoi Diagram, Doubly Stochastic Matrices, Latin Squares, Linear Programming, Polynomiography 1 Introduction Polynomials are undoubtedly one of the most significant objects in all of mathematics and the sciences, particularly in combinatorics. -
IPG Spring 2020 Games Titles - December 2019 Page 1
Games Titles Spring 2020 {IPG} A Puzzle a Day A Collection of Mathematical Problems for Every Day of the School Year Vivian Lucas Summary Although primarily written for pupils ged 11-16, these puzzles do not require a high level of syllabus knowledge, making them accessible to a wide range of ages and abilities.Two levels of difficulty are provided for each entry. There are 180 puzzles, offering two similar ones on each of a wide variety of topics. They can Tarquin Group be used as a daily displayed competition for pupils to enter and a winner can be picked from the days entries. 9781899618521 Pub Date: 3/1/02 It helps to increase interest, to reinforce mathematical vocabulary and of course the puzzles are fun to do. $11.95 USD Complete with answers. Discount Code: LON Trade Paperback Contributor Bio 95 Pages Vivian Lucas is a former head of Mathematics at a school in Derby, UK. Her creative books have been used by Carton Qty: 0 tens of thousands of teachers worldwide in millions of lessons. Education / Teaching Methods & Materials EDU029010 5.5 in H | 5.5 in W Mathematical Snacks A Collection of Interesting Ideas to Fill Those Spare Moments Jon Millington Summary A collection of interesting topics and ideas to fill spare moments... 45 topics and mathematical ideas for the classroom or home, which are quick to introduce and set up but also genuinely stimulating and enriching. Although primarily designed to fill spare moments in normal lessons, they enliven clubs, quizzes and end of Tarquin Group term activities. -
AMS Council Minutes
American Mathematical Society Council Minutes Chicago, Illinois 24 April 2010 at noon Prepared 13 May 2010 Abstract The Council of the Society met at noon on Saturday, 24 April 2010, in the Chicago Room of the Chicago O’Hare Hilton Hotel, O’Hare International Airport, Chicago, IL, 60666.These are the minutes of that meeting. Although some items were treated in Executive Session, all actions taken are reported in these minutes. Council Minutes 24 April 2010 Page 5 I. MINUTES 1. Call to Order 1.1. Opening of the Meeting and Introductions AMS President George Andrews called the meeting to order promptly at noon, CDT, and presided throughout. He asked those present to introduce themselves. Other Council members present were: Alejandro Adem, Georgia Benkart, Sylvain E. Cappell, Ralph L. Cohen, Robert J. Daverman, John M. Franks, Eric M. Friedlander, Robert Guralnick, Richard Hain, Bryna Kra, William A. Massey, Frank Morgan, Jennifer Schultens, Chi-Wang Shu, Joseph H. Silverman, Ronald M. Solomon, Panagiotis E. Souganidis, Janet Talvacchia, Christophe Thiele, Michelle L. Wachs, Steven H. Weintraub, Sarah J. Witherspoon, and David Wright. Other interested parties and guests were: Sandy Golden (Administrative Assistant, AMS Secretary), Sheldon H. Katz (Chair, AMS Nominating Committee), Ellen Maycock (AMS Associate Executive Director), Donald McClure (AMS Executive Director), and Ronald J. Stern (AMS Board of Trustees). Steven Weintraub was the voting Associate Secretary. 1.2. 2009 Elections and More Newly elected or appointed members of the Council took office on 01 February 2010, and they are: President Elect Eric Friedlander Vice President: Sylvain Cappell Members at Large Alejandro Adem Richard Hain Jennifer Schultens Janet Talvacchia Christophe Thiele Math Reviews Editorial Committee Chair Ronald M. -
Alternating Sign Matrices, Extensions and Related Cones
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/311671190 Alternating sign matrices, extensions and related cones Article in Advances in Applied Mathematics · May 2017 DOI: 10.1016/j.aam.2016.12.001 CITATIONS READS 0 29 2 authors: Richard A. Brualdi Geir Dahl University of Wisconsin–Madison University of Oslo 252 PUBLICATIONS 3,815 CITATIONS 102 PUBLICATIONS 1,032 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Combinatorial matrix theory; alternating sign matrices View project All content following this page was uploaded by Geir Dahl on 16 December 2016. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Alternating sign matrices, extensions and related cones Richard A. Brualdi∗ Geir Dahly December 1, 2016 Abstract An alternating sign matrix, or ASM, is a (0; ±1)-matrix where the nonzero entries in each row and column alternate in sign, and where each row and column sum is 1. We study the convex cone generated by ASMs of order n, called the ASM cone, as well as several related cones and polytopes. Some decomposition results are shown, and we find a minimal Hilbert basis of the ASM cone. The notion of (±1)-doubly stochastic matrices and a generalization of ASMs are introduced and various properties are shown. For instance, we give a new short proof of the linear characterization of the ASM polytope, in fact for a more general polytope. -
A Conjecture About Dodgson Condensation
Advances in Applied Mathematics 34 (2005) 654–658 www.elsevier.com/locate/yaama A conjecture about Dodgson condensation David P. Robbins ∗ Received 19 January 2004; accepted 2 July 2004 Available online 18 January 2005 Abstract We give a description of a non-archimedean approximate form of Dodgson’s condensation method for computing determinants and provide evidence for a conjecture which predicts a surprisingly high degree of accuracy for the results. 2005 Elsevier Inc. All rights reserved. In 1866 Charles Dodgson, usually known as Lewis Carroll, proposed a method, that he called condensation [2] for calculating determinants. Dodgson’s method is based on a determinantal identity. Suppose that n 2 is an integer and M is an n by n square matrix with entries in a ring and that R, S, T , and U are the upper left, upper right, lower left, and lower right n − 1byn − 1 square submatrices of M and that C is the central n − 2by n − 2 submatrix. Then it is known that det(C) det(M) = det(R) det(U) − det(S) det(T ). (1) Here the determinant of a 0 by 0 matrix is conventionally 1, so that when n = 2, Eq. (1) is the usual formula for a 2 by 2 determinant. David Bressoud gives an interesting discussion of the genesis of this identity in [1, p. 111]. Dodgson proposes to use this identity repeatedly to find the determinant of M by computing all of the connected minors (determinants of square submatrices formed from * Correspondence to David Bressoud. E-mail address: [email protected] (D. -
Pattern Avoidance in Alternating Sign Matrices
PATTERN AVOIDANCE IN ALTERNATING SIGN MATRICES ROBERT JOHANSSON AND SVANTE LINUSSON Abstract. We generalize the definition of a pattern from permu- tations to alternating sign matrices. The number of alternating sign matrices avoiding 132 is proved to be counted by the large Schr¨oder numbers, 1, 2, 6, 22, 90, 394 . .. We give a bijection be- tween 132-avoiding alternating sign matrices and Schr¨oder-paths, which gives a refined enumeration. We also show that the 132, 123- avoiding alternating sign matrices are counted by every second Fi- bonacci number. 1. Introduction For some time, we have emphasized the use of permutation matrices when studying pattern avoidance. This and the fact that alternating sign matrices are generalizations of permutation matrices, led to the idea of studying pattern avoidance in alternating sign matrices. The main results, concerning 132-avoidance, are presented in Section 3. In Section 5, we enumerate sets of alternating sign matrices avoiding two patterns of length three at once. In Section 6 we state some open problems. Let us start with the basic definitions. Given a permutation π of length n we will represent it with the n×n permutation matrix with 1 in positions (i, π(i)), 1 ≤ i ≤ n and 0 in all other positions. We will also suppress the 0s. 1 1 3 1 2 1 Figure 1. The permutation matrix of 132. In this paper, we will think of permutations in terms of permutation matrices. Definition 1.1. (Patterns in permutations) A permutation π is said to contain a permutation τ as a pattern if the permutation matrix of τ is a submatrix of π. -
Curriculum Vita
CURRICULUM VITA James A. Sellers, Ph.D. Professor Department of Mathematics and Statistics University of Minnesota Duluth Duluth, MN 55812 Phone 218-726-8254 E–mail [email protected] URL http://www.d.umn.edu/~jsellers EDUCATION Bachelor of Science Mathematics, University of Texas at San Antonio, San Antonio, TX, May 1987 Doctor of Philosophy Mathematics, The Pennsylvania State University, University Park, PA, August 1992 Thesis: A Generalization of the Partition Function Research Advisor: Dr. David M. Bressoud PROFESSIONAL EXPERIENCE 2021–present Professor, Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN 2019–2021 Professor and Head, Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN 2009–2019 Professor and Director, Undergraduate Mathematics, The Pennsylvania State University, University Park, PA 2004–2009 Associate Professor and Director, Undergraduate Mathematics, The Pennsylvania State University, University Park, PA 2001–2004 Assistant Professor and Director, Undergraduate Mathematics, The Pennsylvania State University, University Park, PA 1998–2001 Associate Professor, Mathematics, Science and Mathematics Department, Cedarville University, Cedarville, OH 1992–1998 Assistant Professor, Mathematics, Science and Mathematics Department, Cedarville University, Cedarville, OH 1999 (Summer) Editor/Writer, Saxon Publishers, Norman, OK 1997 (Summer) Researcher, Institute for Defense Analysis, La Jolla, CA 1994, 1995, 2001 Mathematics Instructor, San Antonio Prefreshman -
Monmouth University West Long Branch, NJ
The Mathematical Association of America New Jersey Section Fall Meeting Monmouth University West Long Branch, NJ Sunday, November 6, 2005 Abstracts and Biographies of Speakers Alternating Sign Matrices David Bressoud, Macalester College This will be an overview of what is known and what is conjectured about Alternating Sign Matrices, a combinatorial structure with ties to partition theory, representation theory, and statistical mechanics. The talk will include an overview of the story of the Alternating Sign Matrix Conjecture, a tale that begins with a Lewis Carroll algorithm for evaluating determinants and ends with Kuperberg’s realization that the square ice model from statistical mechanics held the key to the solution. David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, MN. He studied with Emil Grosswald at Temple University and taught at Penn State (1977–1994). He has received the MAA Distinguished Teaching Award (Allegheny Mountain Section), the MAA Beckenbach Book Award for Proofs and Confirmations, and has served as MAA Polya Lecturer, 2002–04. He has published over fifty research articles. Other books include Factorization and Primality Testing, Second Year Calculus from Celestial Mechanics to Special Relativity, A Radical Approach to Real Analysis, and, with Stan Wagon, A Course in Computational Number Theory. He chairs CUPM and has served as chair of the AP Calculus Development Committee. Packing Equal Discs in the Plane Ronald Graham, University of California - San Diego A classical problem in geometry deals with finding the densest packings of equal discs in the Euclidean plane. While the solution to this problem has been known for more than a hundred years (hexagonal is best), there are many variations of this problem which are completely unsolved.