Bressoud's conjecture

Sun Kim

doi:10.1016/j.aim.2017.12.004

Bressoud's conjecture

Sun Kim

Department of Mathematics

University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Journal article › peer-review

6 Scopus citations

Abstract

In 1980, D. M. Bressoud obtained an analytic generalization of the Rogers–Ramanujan–Gordon identities. He then tried to establish a combinatorial interpretation of his identity, which specializes to many well-known Rogers–Ramanujan type identities. He proved that a certain partition identity follows from his identity in a very restrictive case and conjectured that the partition identity holds true in general. In this paper, we prove Bressoud's conjecture for the general case by providing bijective proofs.

Original language	English
Pages (from-to)	770-813
Number of pages	44
Journal	Advances in Mathematics
Volume	325
DOIs	https://doi.org/10.1016/j.aim.2017.12.004
State	Published - 2018.02.5

Keywords

Bressoud's conjecture
Integer partitions
Rogers–Ramanujan identities
Rogers–Ramanujan–Gordon–Andrews identities

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10.1016/j.aim.2017.12.004

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title = "Bressoud's conjecture",

abstract = "In 1980, D. M. Bressoud obtained an analytic generalization of the Rogers–Ramanujan–Gordon identities. He then tried to establish a combinatorial interpretation of his identity, which specializes to many well-known Rogers–Ramanujan type identities. He proved that a certain partition identity follows from his identity in a very restrictive case and conjectured that the partition identity holds true in general. In this paper, we prove Bressoud's conjecture for the general case by providing bijective proofs.",

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N2 - In 1980, D. M. Bressoud obtained an analytic generalization of the Rogers–Ramanujan–Gordon identities. He then tried to establish a combinatorial interpretation of his identity, which specializes to many well-known Rogers–Ramanujan type identities. He proved that a certain partition identity follows from his identity in a very restrictive case and conjectured that the partition identity holds true in general. In this paper, we prove Bressoud's conjecture for the general case by providing bijective proofs.

AB - In 1980, D. M. Bressoud obtained an analytic generalization of the Rogers–Ramanujan–Gordon identities. He then tried to establish a combinatorial interpretation of his identity, which specializes to many well-known Rogers–Ramanujan type identities. He proved that a certain partition identity follows from his identity in a very restrictive case and conjectured that the partition identity holds true in general. In this paper, we prove Bressoud's conjecture for the general case by providing bijective proofs.

KW - Bressoud's conjecture

KW - Integer partitions

KW - Rogers–Ramanujan identities

KW - Rogers–Ramanujan–Gordon–Andrews identities

UR - https://www.scopus.com/pages/publications/85038219598

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DO - 10.1016/j.aim.2017.12.004

M3 - Journal article

AN - SCOPUS:85038219598

SN - 0001-8708

VL - 325

SP - 770

EP - 813

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Bressoud's conjecture

Abstract

Keywords

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