Bijective enumeration of some colored permutations given by the product of two long cycles

DOI10.1016/j.disc.2011.09.010zbMath1233.05012arXiv1006.3474OpenAlexW2086026392WikidataQ114190767 ScholiaQ114190767MaRDI QIDQ658051

Ekaterina A. Vassilieva, Valentin Féray

Publication date: 11 January 2012

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

Full work available at URL: https://arxiv.org/abs/1006.3474

zbMATH Keywords

colored permutationsbipartite mapslong cycle factorization

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10) Permutation groups (20B99)

Related Items (4)

A versatile combinatorial approach of studying products of long cycles in symmetric groups ⋮ Combinatorially refine a Zagier-Stanley result on products of permutations ⋮ On products of long cycles: short cycle dependence and separation probabilities ⋮ On products of permutations with the most uncontaminated cycles by designated labels

Cites Work

• An analogue of the Harer-Zagier formula for unicellular maps on general surfaces
• Stanley's formula for characters of the symmetric group.
• A bijective proof of Jackson's formula for the number of factorizations of a cycle
• Annular embeddings of permutations for arbitrary genus
• An analog of the Harer-Zagier formula for unicellular bicolored maps
• Nombre de représentations d'une permutation comme produit de deux cycles de longueurs données
• Factoring \(n\)-cycles and counting maps of given genus
• Irreducible symmetric group characters of rectangular shape.
• Two enumerative results on cycles of permutations
• A direct bijection for the Harer-Zagier formula
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