The "Shape" of q-Binomial Coefficients

2025/05/12 by Harman, Nate
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.08024

Abstract

This is an informal and mostly expository note describing some asymptotic behavior and qualitative properties of the q-binomial coefficients. The results are mostly not new, but the overall story we present does not seem to be well known -- and the diagrams are all new.

Related

• The negative q-binomial
• The q-Binomial Coefficient for Negative Arguments and Some q-Binomial Summation Identities
• q-Binomials and related symmetric unimodal polynomials
• A generalization of the Gaussian formula and a q-analog of Fleck's congruence
• Interesting Deformed q-Series Involving The Central Fibonomial Coefficient