Bijective Proofs of Partition Identities of Macmahon, Andrews, and Subbarao Shishuo Fu, James Sellers
Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao Shishuo Fu, James Sellers To cite this version: Shishuo Fu, James Sellers. Bijective Proofs of Partition Identities of MacMahon, Andrews, and Sub- barao. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.289-296. hal-01207610 HAL Id: hal-01207610 https://hal.inria.fr/hal-01207610 Submitted on 1 Oct 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. FPSAC 2014, Chicago, USA DMTCS proc. AT, 2014, 289{296 Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao Shishuo Fu1∗y and James A. Sellers2z 1Chongqing University, P.R. China 2Penn State University, University Park, USA Abstract. We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to 2; 3; 4; 6 (mod 6), together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result. R´esum´e. Nous revisitons un th´eor`emede partitions d'entiers d^u`aMacMahon, qui relie les partitions dont chaque part est r´ep´et´eeau moins une fois et celles dont les parts sont congrues `a2; 3; 4; 6 (mod 6), ainsi qu'une g´en´eralisationpar Andrews et deux autres par Subbarao.
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