Andrew Timothy Wilson - An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions

dmtcs:2405 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2405
An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions

Authors: Andrew Timothy Wilson 1

  • 1 University of California [San Diego]

A classical result of MacMahon states that inversion number and major index have the same distribution over permutations of a given multiset. In this work we prove a strengthening of this theorem originally conjectured by Haglund. Our result can be seen as an equidistribution theorem over the ordered partitions of a multiset into sets, which we call ordered multiset partitions. Our proof is bijective and involves a new generalization of Carlitz's insertion method. As an application, we develop refined Macdonald polynomials for hook shapes. We show that these polynomials are symmetric and give their Schur expansion.


Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: inversion number,major index,permutation statistics,insertion method,ordered multiset partitions,Macdonald polynomials,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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Source : ScholeXplorer IsRelatedTo ARXIV 1408.5817
Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.jcta.2015.03.012
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1408.5817
  • 1408.5817
  • 10.1016/j.jcta.2015.03.012
  • 10.1016/j.jcta.2015.03.012
  • 10.48550/arxiv.1408.5817
An extension of MacMahon's equidistribution theorem to ordered set partitions

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