Descent sets on 321-avoiding involutions and hook decompositions of partitions

DOI10.1016/j.jcta.2014.08.002zbMath1301.05026arXiv1401.3011OpenAlexW1985237288MaRDI QIDQ458291

Marilena Barnabei, Matteo Silimbani, Flavio Bonetti, Sergi Elizalde

Publication date: 7 October 2014

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

Full work available at URL: https://arxiv.org/abs/1401.3011

zbMATH Keywords

descentlattice pathmajor indexinteger partitionrestricted involution

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Combinatorial aspects of partitions of integers (05A17)

Related Items (15)

The degree of symmetry of lattice paths ⋮ Unimodal permutations and almost-increasing cycles ⋮ Inversion formulae on permutations avoiding 321 ⋮ Measuring symmetry in lattice paths and partitions ⋮ Enumeration on row-increasing tableaux of shape \(2 \times n\) ⋮ Visibility in restricted involutions ⋮ Pattern avoidance and Young tableaux ⋮ Folding phenomenon of major-balance identities on restricted involutions ⋮ Wave linked partitions and 312-avoiding permutations with primacy being 1 ⋮ The Schützenberger involution over Dyck paths ⋮ Combinatorics of fully commutative involutions in classical Coxeter groups ⋮ Families of major index distributions: closed forms and unimodality ⋮ Bijections for pairs of non-crossing lattice paths and walks in the plane ⋮ Two refined major-balance identities on 321-avoiding involutions ⋮ Two descent statistics over \(321\)-avoiding centrosymmetric involutions

Uses Software

• OEIS
• AARON

Cites Work

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• Inversion polynomials for 321-avoiding permutations
• Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns
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• Bijections for refined restricted permutations
• Mahonian pairs
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• Refined restricted involutions
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• On bijections for pattern-avoiding permutations
• Strong versions of Sperner's theorem
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• A simple and unusual bijection for Dyck paths and its consequences
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• Multiple pattern avoidance with respect to fixed points and excedances
• Decreasing subsequences in permutations and Wilf equivalence for involutions
• The Eulerian distribution on involutions is indeed unimodal
• The descent statistic on involutions is not log-concave
• Enumeration of plane partitions
• Longest Increasing and Decreasing Subsequences
• The Eulerian distribution on self evacuated involutions
• Algebraic Combinatorics
• Quelques remarques sur une Construction de Schensted.
• Restricted permutations

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