Year: 2025
Type: article
Abstract: This paper investigates the interplay between numerical semigroups and enumerative combinatorics through the lens of Young diagrams, rook polynomials, and the Lah numbers. For a given numerical semigroup S, we associate a Young diagram constructed from the gap set of S. We then compute the rook polynomial corresponding to this diagram and analyze its coefficients. It is observed that these coefficients exhibit a strong connection with the Lah numbers, which count ordered partitions. Our approach introduces a new combinatorial interpretation of numerical semigroup gaps and reveals novel structural links between algebraic and enumerative concepts.
Author: Meral Süer
Institution: Batman University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4415937697