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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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
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 06 Oct 2018 11:28
Last Modified: 26 Apr 2022 10:26
URI: https://research.sabanciuniv.edu/id/eprint/36609

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