Combinatorial proofs of generating function identities for F-partitions

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

In his memoir in 1984, George E. Andrews introduces many general classes of Frobenius partitions (simply F-partitions). Especially, he focuses his interest on two general classes of F-partitions: one is F-partitions that allow up to k repetitions of an integer in any row, and the other is F-partitions whose parts are taken from k copies of the nonnegative integers. The latter are called k colored F-partitions or F-partitions with k colors. Andrews derives the generating functions of the number of F-partitions with k repetitions and F-partitions with k colors of n and leaves their purely combinatorial proofs as open problems. The primary goal of this article is to provide combinatorial proofs in answer to Andrews' request.

Original languageEnglish (US)
Pages (from-to)217-228
Number of pages12
JournalJournal of Combinatorial Theory. Series A
Volume102
Issue number1
DOIs
StatePublished - Apr 2003

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Fingerprint Dive into the research topics of 'Combinatorial proofs of generating function identities for F-partitions'. Together they form a unique fingerprint.

  • Cite this