Constant terms, jagged partitions, and partitions with difference two at distance two
type: Item
instance of: scholarly article
title: Constant terms, jagged partitions, and partitions with difference two at distance two
zbMATH Open document ID: 1125.11056
author: Jeremy Lovejoy
published in: Aequationes Mathematicae
publication date: 2007-02-14T00:00:00Z
review text: Following \textit{J.-F. Fortin}, \textit{P. Jacob} and \textit{P. Mathieu} [Ramanujan J. 10, No. 2, 215--235 (2005; Zbl 1079.05003); Electron. J. Comb. 12, No. 1, Research paper R12, 17 p., electronic only (2005; Zbl 1062.05011); J. Phys. A, Math. Gen. 38, No. 8, 1699--1709 (2005; Zbl 1061.81068)], a jagged partition refers to an ordered collection of nonnegative integers \((n_1,n_2,\dots, n_n)\) with \(n_n\geq p\) for some positive integer \(p\), further subject to some weakly decreasing conditions that prevent it from being a genuine partition. The prototypical example, which first arose in the study of graded parafermions in mathematical physics, is the 01-jagged partition, corresponding to \(p=1\) and the conditions \(n_i\geq n_{i+1}-1\) and \(n_i\geq n_{i+2}\). In the paper under review the author establishes a group of constant term identities that contain generating functions for jagged partitions and interprets these identities as theorems about partitions with difference \(\geq 2\) at distance 2.
reviewed by: Mihály Szalay
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P82
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 5126571
zbMATH Keywords: Jagged partitions
zbMATH Keywords: constant term identities
zbMATH Keywords: partitions with difference two at distance two
zbMATH Keywords: Capparelli theorem
zbMATH Keywords: Rogers-Ramanujan identities
MaRDI profile type: Publication
full work available at URL: s00010-006-2834-x
OpenAlex ID: W1997867898
DOI: 10.1007/S00010-006-2834-X
Recommended article: On the structure of partition which the difference of their representation function is a constant
Recommended article: Über Partitionen mit Differenzenbedingungen
Recommended article: Constant sum partition of sets of integers and distance magic graphs
Recommended article: Partitions with part difference conditions and Bressoud's conjecture
Recommended article: Partitions with difference conditions and Alder's conjecture
Recommended article: GENERALISATION OF A RESULT ON DISTINCT PARTITIONS WITH BOUNDED PART DIFFERENCES
Recommended article: On constant sum partitions and applications to distance magic-type graphs
Recommended article: Jagged partitions and lattice paths
Recommended article: On some infinite families of congruences for \([j, k]\)-partitions into even parts distinct
Recommended article: A curious identity and its applications to partitions with bounded part differences
description: scientific article; zbMATH DE number 5126571