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A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

An open problem introduced by J. Haglund was to find a bijective proof over Dyck paths that would interchange two of its statistics. This problem was known to be The Symmetry Problem of the q,t-Catalan polynomial and was proven by other means to be true. This project is an attempt to find a bijection, where we provide the bijection's behaviour under certain constrains. Then, we introduce an attempt to translate the problem from Dyck paths to other combinatorial structures. Finally we try to solve a related conjecture, called The Symmetry Problem of parking functions, which generalizes the previous problem. Some results we obtained from The Symmetry Problem of parking functions helped us characterize part of a bijective proof for Dyck paths.

Place, publisher, year, edition, pages
TRITA-MAT-E, 2015:34
National Category
URN: urn:nbn:se:kth:diva-168588OAI: diva2:820906
Subject / course
Educational program
Master of Science - Mathematics
Available from: 2015-06-12 Created: 2015-06-05 Last updated: 2015-06-12Bibliographically approved

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