A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics

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 bijectio...

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Main Author:	Ammar, Ofir
Format:	Others
Language:	English
Published:	KTH, Matematik (Avd.) 2015
Online Access:	http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-168588

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spelling	ndltd-UPSALLA1-oai-DiVA.org-kth-1685882015-06-13T04:56:16ZA thesis submitted in fulfilment of the requirements for the degree of Masters of MathematicsengAmmar, OfirKTH, Matematik (Avd.)2015An 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. Student thesisinfo:eu-repo/semantics/bachelorThesistexthttp://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-168588TRITA-MAT-E ; 2015:34application/pdfinfo:eu-repo/semantics/openAccess
collection	NDLTD
language	English
format	Others
sources	NDLTD
description	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.
author	Ammar, Ofir
spellingShingle	Ammar, Ofir A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics
author_facet	Ammar, Ofir
author_sort	Ammar, Ofir
title	A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics
title_short	A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics
title_full	A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics
title_fullStr	A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics
title_full_unstemmed	A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics
title_sort	thesis submitted in fulfilment of the requirements for the degree of masters of mathematics
publisher	KTH, Matematik (Avd.)
publishDate	2015
url	http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-168588
work_keys_str_mv	AT ammarofir athesissubmittedinfulfilmentoftherequirementsforthedegreeofmastersofmathematics AT ammarofir thesissubmittedinfulfilmentoftherequirementsforthedegreeofmastersofmathematics
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A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics

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