The negative q-binomial
Shishuo Fu, Victor Reiner, Dennis Stanton, and Nathaniel Thiem
TL;DR
This paper explores the properties and interpretations of the q-binomial coefficient at -q, introduces a (q,t)-generalization, and presents an example of cyclic sieving involving unitary spaces.
Contribution
It provides new insights into the q-binomial coefficient at negative values and establishes a (q,t)-version with applications to cyclic sieving phenomena.
Findings
Interpretations for the q-binomial coefficient at -q are discussed.
A (q,t)-version of the q-binomial coefficient is established.
An instance of cyclic sieving involving unitary spaces is presented.
Abstract
Interpretations for the q-binomial coefficient evaluated at -q are discussed. A (q,t)-version is established, including an instance of a cyclic sieving phenomenon involving unitary spaces.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Algebraic structures and combinatorial models