{"title":"A bijection related to Bressoud's conjecture","authors":"Y.H. Chen, Thomas Y. He","doi":"10.1016/j.jcta.2025.106032","DOIUrl":null,"url":null,"abstract":"<div><div>Bressoud introduced the partition function <span><math><mi>B</mi><mo>(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>;</mo><mi>η</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>r</mi><mo>;</mo><mi>n</mi><mo>)</mo></math></span>, which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition function <span><math><mi>B</mi><mo>(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>;</mo><mi>η</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>r</mi><mo>;</mo><mi>n</mi><mo>)</mo></math></span> in multi-summation form. In this article, we introduce a bijection related to Bressoud's conjecture. As an application, we give the proof of a companion to the Göllnitz-Gordon identities.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"214 ","pages":"Article 106032"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316525000275","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Bressoud introduced the partition function , which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition function in multi-summation form. In this article, we introduce a bijection related to Bressoud's conjecture. As an application, we give the proof of a companion to the Göllnitz-Gordon identities.
期刊介绍:
The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.