Constant terms, jagged partitions, and partitions with difference two at distance two
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.
partitions with difference two at distance two
scientific article; zbMATH DE number 5126571