On a Conjecture of Hanna Connecting Distinct Part and Complete Partitions

George E. Andrews; George Beck; Brian Hopkins

doi:10.1007/s00026-019-00476-1

On a Conjecture of Hanna Connecting Distinct Part and Complete Partitions

George E. Andrews, George Beck, Brian Hopkins

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	217-224
Number of pages	8
Journal	Annals of Combinatorics
Volume	24
Issue number	2
DOIs	https://doi.org/10.1007/s00026-019-00476-1
State	Published - Jun 1 2020

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1007/s00026-019-00476-1

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abstract = "Complete partitions are a generalization of MacMahon{\textquoteright}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.",

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AU - Hopkins, Brian

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N2 - 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.

AB - 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.

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On a Conjecture of Hanna Connecting Distinct Part and Complete Partitions

Abstract

All Science Journal Classification (ASJC) codes

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