On Integer Partitions with a Fixed Overlined Smallest Part

George E. Andrews; Mohamed El Bachraoui

doi:10.1007/s00026-025-00798-3

On Integer Partitions with a Fixed Overlined Smallest Part

George E. Andrews
, Mohamed El Bachraoui

Department of Mathematical Sciences

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

Abstract

We consider a sequence of integer partitions wherein the smallest part is fixed and its first occurrence may be overlined. Among the results, we prove identities and positivity for this sequence and its weighted versions. As a consequence, we deduce inequalities of integer partitions and we establish Legendre type formulas. Furthermore, we give a full description modulo 2 for our sequences.

Original language	English
Journal	Annals of Combinatorics
DOIs	https://doi.org/10.1007/s00026-025-00798-3
Publication status	Accepted/In press - 2025

Keywords

Partitions
Positive q-series
q-series

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Access to Document

10.1007/s00026-025-00798-3

Cite this

@article{6ea7b94b0c0d47e980c98fa4f9471ec7,

title = "On Integer Partitions with a Fixed Overlined Smallest Part",

abstract = "We consider a sequence of integer partitions wherein the smallest part is fixed and its first occurrence may be overlined. Among the results, we prove identities and positivity for this sequence and its weighted versions. As a consequence, we deduce inequalities of integer partitions and we establish Legendre type formulas. Furthermore, we give a full description modulo 2 for our sequences.",

keywords = "Partitions, Positive q-series, q-series",

author = "Andrews, \{George E.\} and \{El Bachraoui\}, Mohamed",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.",

year = "2025",

doi = "10.1007/s00026-025-00798-3",

language = "English",

journal = "Annals of Combinatorics",

issn = "0218-0006",

publisher = "Springer International Publishing",

}

TY - JOUR

T1 - On Integer Partitions with a Fixed Overlined Smallest Part

AU - Andrews, George E.

AU - El Bachraoui, Mohamed

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

PY - 2025

Y1 - 2025

N2 - We consider a sequence of integer partitions wherein the smallest part is fixed and its first occurrence may be overlined. Among the results, we prove identities and positivity for this sequence and its weighted versions. As a consequence, we deduce inequalities of integer partitions and we establish Legendre type formulas. Furthermore, we give a full description modulo 2 for our sequences.

AB - We consider a sequence of integer partitions wherein the smallest part is fixed and its first occurrence may be overlined. Among the results, we prove identities and positivity for this sequence and its weighted versions. As a consequence, we deduce inequalities of integer partitions and we establish Legendre type formulas. Furthermore, we give a full description modulo 2 for our sequences.

KW - Partitions

KW - Positive q-series

KW - q-series

UR - https://www.scopus.com/pages/publications/105024924542

UR - https://www.scopus.com/pages/publications/105024924542#tab=citedBy

U2 - 10.1007/s00026-025-00798-3

DO - 10.1007/s00026-025-00798-3

M3 - Article

AN - SCOPUS:105024924542

SN - 0218-0006

JO - Annals of Combinatorics

JF - Annals of Combinatorics

ER -

On Integer Partitions with a Fixed Overlined Smallest Part

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this