Shifted and Shiftless Partition Identities II
| dc.creator | Garvan, Frank G. | |
| dc.creator | Yesilyurt, Hamza | |
| dc.date | 2006-05-12 | |
| dc.date.accessioned | 2026-07-07T07:14:09Z | |
| dc.date.available | 2026-07-07T07:14:09Z | |
| dc.description | Let S and T be sets of positive integers and let a be a fixed positive integer. An a-shifted partition identity has the form p(S,n)=p(T,n-a), for all n greater or equal to a. Here p(S,n) is the number partitions of n whose parts are elements of S. For all known nontrivial shifted partition identities, the sets S and T are unions of arithmetic progressions modulo M for some M. In 1987, Andrews found two 1-shifted examples (M=32, 40) and asked whether there were any more. In 1989, Kalvade responded with a further six. In 2000, the first author found 59 new 1-shifted identities using a computer search and showed how these could be proved using the theory of modular functions. Modular transformation of certain shifted identities leads to shiftless partition identities. Again let a be a fixed positive integer, and S, T be distinct sets of positive integers. A shiftless partition identity has the form p(S,n)=p(T,n), for all n not equal to a. In this paper, we show, except in one case, how all known 1-shifted and shiftless identities follow from a four parameter theta function identity due to Jacobi. New shifted and shiftless partition identities are proved. | |
| dc.description | To appear in Int. J. Number Theory | |
| dc.identifier | https://arxiv.org/abs/math/0605317 | |
| dc.identifier | http://arxiv.org/abs/math/0605317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112755 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Primary: 11P83; Secondary: 05A17 | |
| dc.title | Shifted and Shiftless Partition Identities II | |
| dc.type | text |