On a Conjecture of Hanna Connecting Distinct Part and Complete Partitions

George E. Andrews, George Beck, Brian Hopkins

Research output: Contribution to journalArticlepeer-review

Abstract

Complete partitions are a generalization of MacMahon’s perfect partitions; we further generalize these by defining k-step partitions. A matrix equation shows an unexpected connection between k-step partitions and distinct part partitions. We provide two proofs of the corresponding theorem, one using generating functions and one combinatorial. The algebraic proof relies on a generalization of a conjecture made by Paul Hanna in 2012.

Original languageEnglish (US)
Pages (from-to)217-224
Number of pages8
JournalAnnals of Combinatorics
Volume24
Issue number2
DOIs
StatePublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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