Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Conference papers

An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions

Abstract : 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.
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Thursday, October 1, 2015 - 9:29:10 AM
Last modification on : Wednesday, August 7, 2019 - 12:18:06 PM
Long-term archiving on: : Saturday, January 2, 2016 - 10:54:52 AM


Publisher files allowed on an open archive




Andrew Timothy Wilson. An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.345-356, ⟨10.46298/dmtcs.2405⟩. ⟨hal-01207606⟩



Record views


Files downloads