Full metadata
Title
A Statistic on a Super Catalan Structure
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.
Date Created
2018-05
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)
Topical Subject
Resource Type
Extent
13 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
Series
Academic Year 2017-2018
Handle
https://hdl.handle.net/2286/R.I.48382
Level of coding
minimal
Cataloging Standards
System Created
- 2018-04-27 12:12:54
System Modified
- 2021-08-11 04:09:57
- 3 years 3 months ago
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