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A Statistic on a Super Catalan Structure

Abstract 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.
Created Date 2018-05
Contributor House, John Douglas (Author) / Fishel, Susanna (Thesis Director) / Childress, Nancy (Committee Member) / School of Mathematical and Statistical Sciences / Barrett, The Honors College
Subject Path Shuffles / Combinatorics / Q Analogue
Series Academic Year 2017-2018
Type Text
Extent 13 pages
Language English
Reuse Permissions All Rights Reserved
Collaborating Institutions Barrett, the Honors College
Additional Formats MODS / OAI Dublin Core / RIS

  House_J_Spring 2018.pdf
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