Card shuffling and \(P\)-partitions

DOI10.1016/j.disc.2021.112448zbMath1480.60012arXiv2004.01659OpenAlexW3162997127MaRDI QIDQ2032872

Jason Fulman, T. Kyle Petersen

Publication date: 14 June 2021

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.01659

zbMATH Keywords

descentscard shuffling\(P\)-partitionpeaks of permutations

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Combinatorial probability (60C05)

Cites Work

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• Analysis of casino shelf shuffling machines
• Derivative polynomials and enumeration of permutations by number of interior and left peaks
• Enriched \(P\)-partitions and peak algebras
• Randomization time for the overhand shuffle
• Orthogonal idempotents in the descent algebra of \(B_ n\) and applications
• Trailing the dovetail shuffle to its lair
• The distribution of descents in fixed conjugacy classes of the symmetric groups
• Hopf algebra of the planar binary trees
• Random walks and hyperplane arrangements
• Affine shuffles, shuffles with cuts, the Whitehouse module, and patience sorting
• Riffle shuffles, cycles, and descents
• A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements
• Plethystic formulas for permutation enumeration
• A historical survey of P-partitions
• Shuffling Cards and Stopping Times
• Enriched 𝑃-Partitions
• Applications of the Brauer complex: card shuffling, permutation statistics, and dynamical systems