An extension of MacMahon's equidistribution theorem to ordered multiset partitions

zbMath1329.05030arXiv1508.06261MaRDI QIDQ907252

Andrew Timothy Wilson

Publication date: 25 January 2016

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.06261

zbMATH Keywords

permutation statisticsMacdonald polynomialsinversion numbermajor indexinsertion methodordered multiset partitions

Mathematics Subject Classification ID

Partitions of sets (05A18) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05)

Related Items (22)

Set superpartitions and superspace duality modules ⋮ Sequences, q-Multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers ⋮ Mahonian and Euler-Mahonian statistics for set partitions ⋮ Higher Specht bases for generalizations of the coinvariant ring ⋮ A valley version of the delta square conjecture ⋮ Ordered set partition statistics and the delta conjecture ⋮ The Haglund-Remmel-Wilson identity for set partitions ⋮ A minimaj-preserving crystal on ordered multiset partitions ⋮ Generalized coinvariant algebras for wreath products ⋮ Vandermondes in superspace ⋮ Vandermondes, superspace, and delta conjecture modules ⋮ \(q\)-Stirling numbers in type \(B\) ⋮ Spanning subspace configurations ⋮ Hall-Littlewood expansions of Schur delta operators at \(t=0\). ⋮ Ordered set partitions, generalized coinvariant algebras, and the delta conjecture ⋮ The generalized Delta conjecture at \(t = 0\) ⋮ A proof of the delta conjecture when \(q=0\) ⋮ Ordered set partitions and the 0-Hecke algebra ⋮ The valley version of the extended delta conjecture ⋮ A flag variety for the Delta Conjecture ⋮ From \(q\)-Stirling numbers to the ordered multiset partitions: a viewpoint from vincular patterns ⋮ Ordered set partitions, Garsia-Procesi modules, and rank varieties

Cites Work

• Unnamed Item
• Statistics on wreath products, perfect matchings, and signed words
• Fix-Mahonian calculus. I: Two transformations
• The general boson normal ordering problem
• Major index for 01-fillings of moon polyominoes
• An extension of MacMahon's equidistribution theorem to ordered set partitions
• A Combinatorial Property of q-Eulerian Numbers
• Some Particular Entries of the Two-Parameter Kostka Matrix
• A combinatorial formula for Macdonald polynomials
• On the Netto Inversion Number of a Sequence

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