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Yee's bijective proof of Bousquet-Mélou and Eriksson's refinement of the lecture hall partition theorem

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Talay, Beril (2018) Yee's bijective proof of Bousquet-Mélou and Eriksson's refinement of the lecture hall partition theorem. [Thesis]

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Official URL: http://risc01.sabanciuniv.edu/record=b1817048 (Table of Contents)

Abstract

A partition (...) of a positive integer N is a lecture hall partition of length n if it satisfies the condition (...). Lecture hall partitions are introduced by Bousquet-Mélou and Eriksson, while studying Coxeter groups and their Poincare series. Bousquet-Mélou and Eriksson showed that the number of lecture hall partitions of length n where the alternating sum of the parts is k equals to the number of partitions into k odd parts which are less than 2n by a combinatorial bijection. Then, Yee also proved the fact by combinatorial bijection which is differently defined for one of the bijections that were suggested by Bousquet-Mélou and Eriksson. In this thesis we give Yee’s proof with details and further possible problems which arise from a paper of Corteel et al.

Item Type:Thesis
Uncontrolled Keywords:Integer partition. -- Lecture hall partitions. -- Partition bijection. -- Partition analysis. -- Tamsayı parçalanışları. -- Amfi parçalanışları. --Parçalanış eşlemeleri. -- Parçalanış analizi.
Subjects:Q Science > QA Mathematics
ID Code:36609
Deposited By:IC-Cataloging
Deposited On:06 Oct 2018 11:28
Last Modified:22 May 2019 14:11

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