Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 056, 12 pages      arXiv:2503.10890      https://doi.org/10.3842/SIGMA.2025.056
Contribution to the Special Issue on Basic Hypergeometric Series Associated with Root Systems and Applications in honor of Stephen C. Milne

Positive Weighted Partitions Generated by Double Series

George E. Andrews a and Mohamed El Bachraoui b
a) The Pennsylvania State University, University Park, Pennsylvania 16802, USA
b) United Arab Emirates University, PO Box 15551, Al-Ain, United Arab Emirates

Received March 14, 2025, in final form July 04, 2025; Published online July 12, 2025

Abstract
We investigate some weighted integer partitions whose generating functions are double-series. We will establish closed formulas for these $q$-double series and deduce that their coefficients are non-negative. This leads to inequalities among integer partitions.

Key words: partitions; $q$-series; positive $q$-series.

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