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

3 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

Access to Document

10.1007/s00026-019-00476-1

Cite this

@article{c804b0b6325643218fa93df50f1a21f3,

title = "On a Conjecture of Hanna Connecting Distinct Part and Complete Partitions",

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.",

author = "Andrews, \{George E.\} and George Beck and Brian Hopkins",

year = "2020",

month = jun,

day = "1",

doi = "10.1007/s00026-019-00476-1",

language = "English (US)",

volume = "24",

pages = "217--224",

journal = "Annals of Combinatorics",

issn = "0218-0006",

publisher = "Springer International Publishing",

number = "2",

}

TY - JOUR

T1 - On a Conjecture of Hanna Connecting Distinct Part and Complete Partitions

AU - Andrews, George E.

AU - Beck, George

AU - Hopkins, Brian

PY - 2020/6/1

Y1 - 2020/6/1

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.

UR - https://www.scopus.com/pages/publications/85078028886

UR - https://www.scopus.com/pages/publications/85078028886#tab=citedBy

U2 - 10.1007/s00026-019-00476-1

DO - 10.1007/s00026-019-00476-1

M3 - Article

AN - SCOPUS:85078028886

SN - 0218-0006

VL - 24

SP - 217

EP - 224

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 2

ER -

On a Conjecture of Hanna Connecting Distinct Part and Complete Partitions

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this