Description
The Super Catalan numbers are a known set of numbers which have so far eluded a combinatorial interpretation. Several weighted interpretations have appeared since their discovery, one of which was discovered by William Kuszmaul in 2017. In this paper, we connect the weighted Super Catalan structure created previously by Kuszmaul and a natural $q$-analogue of the Super Catalan numbers. We do this by creating a statistic $\sigma$ for which the $q$ Super Catalan numbers, $S_q(m,n)=\sum_X (-1)^{\mu(X)} q^{\sigma(X)}$. In doing so, we take a step towards finding a strict combinatorial interpretation for the Super Catalan numbers.
Details
Contributors
- House, John Douglas (Author)
- Fishel, Susanna (Thesis director)
- Childress, Nancy (Committee member)
- School of Mathematical and Statistical Sciences (Contributor)
- Barrett, The Honors College (Contributor)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2018-05
Topical Subject
Resource Type
Language
- eng