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

DOI10.1016/j.jcta.2015.03.012zbMath1315.05019arXiv1408.5817OpenAlexW2963427644MaRDI QIDQ2347981

Andrew Timothy Wilson, Jeffery B. Remmel

Publication date: 10 June 2015

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.5817

zbMATH Keywords

Stirling numbersbijectionmajor indexinversionsordered set partitions

Mathematics Subject Classification ID

Partitions of sets (05A18) Bell and Stirling numbers (11B73)

Related Items

Set superpartitions and superspace duality modules, A weighted sum over generalized Tesler matrices, Mahonian and Euler-Mahonian statistics for set partitions, A valley version of the delta square conjecture, Ordered set partition statistics and the delta conjecture, Decorated Dyck Paths, Polyominoes, and the Delta Conjecture, The Haglund-Remmel-Wilson identity for set partitions, An inversion statistic on the generalized symmetric groups, Some identities involving \(q\)-Stirling numbers of the second kind in type B, \(q\)-Stirling numbers in type \(B\), An extension of MacMahon's equidistribution theorem to ordered multiset partitions, The Delta Conjecture, The Haglund-Remmel-Wilson identity for \(k\)-Stirling permutations, Ordered set partitions, generalized coinvariant algebras, and the delta conjecture, A new bijective proof of Babson and Steingrímsson's conjecture, A proof of the delta conjecture when \(q=0\), Ordered set partitions and the 0-Hecke algebra, Ordered set partitions and the 0-Hecke algebra, MacMahon's equidistribution theorem for \(k\)-Stirling permutations, Unnamed Item, Spanning line configurations, Delta conjectures, A flag variety for the Delta Conjecture, From \(q\)-Stirling numbers to the ordered multiset partitions: a viewpoint from vincular patterns, Further extensions of Haglund-Remmel-Wilson identity

Cites Work

• Unnamed Item
• Statistics on wreath products, perfect matchings, and signed words
• \(p,q\)-Stirling numbers and set partition statistics
• Euler-Mahonian statistics on ordered set partitions. II.
• Q-counting rook configurations and a formula of Frobenius
• The r-major index
• A \(q\)-analog of Newton's series, Stirling functions and Eulerian functions
• Euler–Mahonian Statistics on Ordered Set Partitions
• A Combinatorial Property of q-Eulerian Numbers
• On the Netto Inversion Number of a Sequence
• The flag major index and group actions on polynomial rings.