Combinatorially refine a Zagier-Stanley result on products of permutations

DOI10.1016/j.disc.2020.111912zbMath1441.05004arXiv1910.01029OpenAlexW3014442971MaRDI QIDQ2185914

Ricky X. F. Chen

Publication date: 8 June 2020

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

Full work available at URL: https://arxiv.org/abs/1910.01029

zbMATH Keywords

exceedancecycle-typeplane permutationproduct of long cyclesZagier-Stanley result

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Permutations, words, matrices (05A05)

Related Items (2)

Random 2-cell embeddings of multistars ⋮ A versatile combinatorial approach of studying products of long cycles in symmetric groups

Cites Work

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• Odd permutations are nicer than even ones
• Bijective enumeration of some colored permutations given by the product of two long cycles
• A new combinatorial identity for unicellular maps, via a direct bijective approach
• Factorization of permutations into n-cycles
• Factoring \(n\)-cycles and counting maps of given genus
• Two enumerative results on cycles of permutations
• Counting rooted maps by genus. I
• Plane Permutations and Applications to a Result of Zagier--Stanley and Distances of Permutations
• Counting Cycles in Permutations by Group Characters, With an Application to a Topological Problem
• On the local genus distribution of graph embeddings
• Separation Probabilities for Products of Permutations

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