A combinatorial identity relating Glass and Ng’s identity to Milne’s identity
Volume 180 / 2026
Colloquium Mathematicum 180 (2026), 51-57
MSC: Primary 05A19
DOI: 10.4064/cm9692-11-2025
Published online: 25 February 2026
Abstract
We prove a combinatorial identity, which implies a connection between an identity of Milne and an identity of Glass and Ng concerning the hook length formula. As applications, we obtain some new formulas on partitions, factorial numbers, rising factorial numbers, falling factorial numbers, and Catalan numbers.
