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- W4307169339 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. This generalization leads to a new extension of Macdonald polynomials for hook shapes. We use our main theorem to show that these polynomials are symmetric and we give their Schur expansion." @default.
- W4307169339 created "2022-10-29" @default.
- W4307169339 creator A5014375002 @default.
- W4307169339 date "2015-08-25" @default.
- W4307169339 modified "2023-09-23" @default.
- W4307169339 title "An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions" @default.
- W4307169339 doi "https://doi.org/10.48550/arxiv.1508.06261" @default.
- W4307169339 hasPublicationYear "2015" @default.
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