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Peter Masso: Klassiska resultat om permutationer

Degree Project for teacher

Tid: Ti 2025-02-04 kl 11.00 - 12.00

Plats: Mittag-Lefflerrummet

Respondent: Peter Masso

Handledare: Per Alexandersson

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Abstract.

This work primarily aims to describe and prove the equal distributional properties of the statistics major index and inversions for permutations—a classical result established by Percy A. MacMahon, a pivotal figure in the development of combinatorics during the late 19th and early 20th centuries. The study explores fundamental theories such as permutations, enumerative statistics on permutations, generating functions, and q-analogues. Key theorems and propositions are proved to establish equidistribution properties between the major index and inversions of permutations. Additionally, the work delves into further intriguing concepts, including Stirling numbers of the first kind, the statistic excedances, and their connections to descents.