Shuffling Decks with Repeated Card Values
Shuffling Decks With Repeated Card Values by Mark A. Conger A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mathematics) in The University of Michigan 2007 Doctoral Committee: Assistant Professor Divakar Viswanath, Chair Professor Sergey Fomin Professor John K. Riles Professor Bruce Sagan, Michigan State University c Mark A. Conger All Rights Reserved 2007 ACKNOWLEDGEMENTS This thesis has been more than 16 years in the making, so there are a lot of people to thank. Thanks to my friends and roommates Steve Blair and Paul Greiner, who managed to get me through my first year at Michigan (1990-91). As Steve said to me once, years later, “Together, we made a pretty good graduate student.” Thanks to Prof. Larry Wright at Williams for teaching me about Radix Sort. And thanks to everyone who shared their punch cards and punch card stories with me: John Remmers, Ken Josenhans, Thom Sterling, and Larry Mohr among others. Thanks to Profs. Bill Lenhart at Williams and Phil Hanlon at Michigan who taught me basic enumerative combinatorics, especially how to switch summation signs. Prof. Ollie Beaver taught me how to use confidence intervals, and Martin Hildebrand taught me the Central Limit Theorem. Pam Walpole and Pete Morasca taught me many things I use every day. Most of the programs used to test hypotheses and generate Monte Carlo data were written in C/C++. The thesis was typeset in LATEX using the PSTricks package, with a number of figures written directly in PostScript. Other figures, as well as the glossary and notation pages, were generated from scripts by Perl programs.
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