New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions

Autor:	Berkovich, Alexander, Uncu, Ali Kemal
Rok vydání:	2016
Předmět:	Mathematics - Number Theory Mathematics - Combinatorics 05A15 05A17 05A19 11B34 11B75 11P81 11P84 33D15
Druh dokumentu:	Working Paper
Popis:	We use the $q$-binomial theorem, the $q$-Gauss sum, and the ${}_2\phi_1 \rightarrow {}_2\phi_2$ transformation of Jackson to discover and prove many new weighted partition identities. These identities involve unrestricted partitions, overpartitions, and partitions with distinct even parts. Smallest part of the partitions plays an important role in our analysis. This work was motivated in part by the research of Krishna Alladi. Comment: 18 pages, 7 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1608.00193 Zobrazit plný text záznamu View this record from Arxiv