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Partitions and hook lengths


Xiong, Huan. Partitions and hook lengths. 2016, University of Zurich, Faculty of Science.

Abstract

The concept of partition is important in combinatorics, number theory and representation theory. It has attracted much attention in past centuries. In this thesis, the difference operators on functions of partitions and strict partitions are introduced to derive many new and classic hook-content formulas. As anapplication, several generalizations of Han-Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to hook lengths and contents are achieved. Many new hook-content formulas for self-conjugate and doubled distinct partitions are also derived. Motivated by number theory and modular representation theory of symmetric groups, t-core partitions are widely studied recently by many mathematicians. This thesis studies simultaneous core partitions and characterizes the largest size of (t; t+1; : : : ; t+p)-core partitions. We also verify Amdeberhan's conjectures on the number, the largest size and the average size of (t; t + 1)-core partitions with distinct parts.

Abstract

The concept of partition is important in combinatorics, number theory and representation theory. It has attracted much attention in past centuries. In this thesis, the difference operators on functions of partitions and strict partitions are introduced to derive many new and classic hook-content formulas. As anapplication, several generalizations of Han-Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to hook lengths and contents are achieved. Many new hook-content formulas for self-conjugate and doubled distinct partitions are also derived. Motivated by number theory and modular representation theory of symmetric groups, t-core partitions are widely studied recently by many mathematicians. This thesis studies simultaneous core partitions and characterizes the largest size of (t; t+1; : : : ; t+p)-core partitions. We also verify Amdeberhan's conjectures on the number, the largest size and the average size of (t; t + 1)-core partitions with distinct parts.

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Additional indexing

Item Type:Dissertation
Referees:Dehaye Paul-Olivier, Han Guo-Niu, Féray Valentin, Nikeghbali Ashkan
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2016
Deposited On:27 Oct 2016 08:06
Last Modified:02 Feb 2018 10:32
Number of Pages:121
OA Status:Closed
Related URLs:https://www.recherche-portal.ch/ZAD:default_scope:ebi01_prod010718674 (Library Catalogue)

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