Stack-sorting, set partitions, and Lassalle's sequence

DOI10.1016/j.jcta.2020.105275zbMath1442.05006arXiv1809.01340OpenAlexW3030809477MaRDI QIDQ778710

Jordan A. Miller, Colin Defant, Michael Engen

Publication date: 3 July 2020

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

Full work available at URL: https://arxiv.org/abs/1809.01340

zbMATH Keywords

Tutte polynomialcumulantset partitionstack-sortingLassalle's sequenceuniquely sorted permutationvalid hook configuration

Mathematics Subject Classification ID

Graph polynomials (05C31) Exact enumeration problems, generating functions (05A15) Partitions of sets (05A18) Permutations, words, matrices (05A05)

Related Items (27)

Stack-sorting for Coxeter groups ⋮ 312-Avoiding reduced valid hook configurations and duck words ⋮ Catalan intervals and uniquely sorted permutations ⋮ Highly sorted permutations and Bell numbers ⋮ Lattice paths and \((n - 2)\)-stack sortable permutations ⋮ Unimodality of a refinement of Lassalle's sequence ⋮ Fertilitopes ⋮ Polyurethane toggles ⋮ Dynamical aspects of \(\sigma\)-machines ⋮ A lift of West's stack-sorting map to partition diagrams ⋮ Stack-sorting preimages of permutation classes ⋮ Uniquely sorted permutations ⋮ The combinatorics of a tree-like functional equation for connected chord diagrams ⋮ Fertility monotonicity and average complexity of the stack-sorting map ⋮ Preimages under the Queuesort algorithm ⋮ Restricted stacks as functions ⋮ Enumeration of Stack-Sorting Preimages via a Decomposition Lemma ⋮ Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations ⋮ Fertility, Strong Fertility, and Postorder Wilf Equivalence ⋮ Troupes, cumulants, and stack-sorting ⋮ Further bijections to pattern-avoiding valid hook configurations ⋮ Stack-sorting with consecutive-pattern-avoiding stacks ⋮ Stack sorting with increasing and decreasing stacks ⋮ Counting 3-stack-sortable permutations ⋮ Preimages under the bubblesort operator ⋮ Stack-sorting for Words ⋮ Troupes, cumulants, and stack-sorting

Cites Work

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• Counting 3-stack-sortable permutations
• Preimages under the stack-sorting algorithm
• Wilf-equivalence for singleton classes
• Cumulants of the q-semicircular Law, Tutte Polynomials, and Heaps
• Combinatorics of Permutations
• Unimodality, log-concavity, real-rootedness and beyond
• Zeta Functions and the Log Behaviour of Combinatorial Sequences
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• Stack-sorting for Words
• On the Interpretation of Whitney Numbers Through Arrangements of Hyperplanes, Zonotopes, Non-Radon Partitions, and Orientations of Graphs
• Lectures on the Combinatorics of Free Probability
• Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations
• A probabilistic interpretation of a sequence related to Narayana polynomials

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