Mahonian pairs

DOI10.1016/j.jcta.2011.11.003zbMath1242.05019arXiv1101.4332OpenAlexW2913426248WikidataQ57432196 ScholiaQ57432196MaRDI QIDQ662027

Bruce E. Sagan, Carla D. Savage

Publication date: 11 February 2012

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

Full work available at URL: https://arxiv.org/abs/1101.4332

zbMATH Keywords

inversion numbermajor indexMahonian statisticinteger partition\(q\)-Catalan numberrank of a partitionballot sequence\(q\)-Fibonacci numberFoata's fundamental bijectionGreene-Kleitman symmetric chain decomposition

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Combinatorial aspects of partitions of integers (05A17)

Related Items

The \(q\)-log-concavity and unimodality of \(q\)-Kaplansky numbers, Counting lattice paths by crossings and major index I: the corner-flipping bijections, Statistics on restricted Fibonacci words, Restricted growth function patterns and statistics, Unimodal permutations and almost-increasing cycles, Eulerian pairs on Fibonacci words, Inversion polynomials for 321-avoiding permutations, Inversion formulae on permutations avoiding 321, Equidistributions of Mahonian statistics over pattern avoiding permutations, Some refinements of Stanley's shuffle theorem, Descent sets on 321-avoiding involutions and hook decompositions of partitions, Counting signed vexillary permutations, On maximal chains in the non-crossing partition lattice, Enumeration on row-increasing tableaux of shape \(2 \times n\), Set partition patterns and statistics, Parabolically induced functions and equidistributed pairs, Major index over descent for pattern-avoiding permutations, Inversion polynomials for permutations avoiding consecutive patterns

Cites Work

• Permutation patterns and statistics
• The decrease value theorem with an application to permutation statistics
• q-hook length formulas for forests
• Binomial determinants, paths, and hook length formulae
• q-Catalan numbers
• Extension of the partition sieve
• Permutation statistics and linear extensions of posets
• On the difference of successive Gaussian polynomials
• Strong versions of Sperner's theorem
• A bijection for partitions with all ranks at least \(t\)
• A recurrence for counting graphical partitions
• A note on graphical partitions
• Variants of the Rogers-Ramanujan identities
• On graphical partitions
• Two element lattice permutation numbers and their \(q\)-generalization
• Factors of the Gaussian coefficients
• Set partition statistics and \(q\)-Fibonacci numbers
• Some formulas related to the Rogers-Ramanujan identities
• Combinatorial Interpretations of Binomial Coefficient Analogues Related to Lucas Sequences
• A Note on the Rogers‐Ramanujan identities
• The limiting distribution of the coefficients of the 𝑞-Catalan numbers
• Examples of noninjectivity for the combinatorial radon transform
• On the Netto Inversion Number of a Sequence
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item