Bijections and symmetries for the factorizations of the long cycle

DOI10.1016/j.aam.2013.01.004zbMath1280.05006arXiv1112.4970OpenAlexW1987001941WikidataQ114214533 ScholiaQ114214533MaRDI QIDQ394753

Alejandro H. Morales, Olivier Bernardi

Publication date: 27 January 2014

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.4970

zbMATH Keywords

Jackson's formulaconstellationsone-face maps

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05) Combinatorial aspects of representation theory (05E10)

Related Items (11)

A character approach to directed genus distribution of graphs: the bipartite single-black-vertex case ⋮ Some probabilistic trees with algebraic roots ⋮ A simple model of trees for unicellular maps ⋮ Calculating the Euler characteristic of the moduli space of curves ⋮ Separation Probabilities for Products of Permutations ⋮ \(\operatorname{GL}_n(\mathbb{F}_q)\)-analogues of factorization problems in the symmetric group ⋮ Unnamed Item ⋮ Factorization problems in complex reflection groups ⋮ A five-element transformation monoid on labelled trees ⋮ Factorization problems in complex reflection groups ⋮ Combinatorial and algebraic enumeration: a survey of the work of Ian P. Goulden and David M. Jackson

Cites Work

• Some probabilistic trees with algebraic roots
• An analogue of the Harer-Zagier formula for unicellular maps on general surfaces
• A bijective proof of Jackson's formula for the number of factorizations of a cycle
• Graphs on surfaces and their applications. Appendix by Don B. Zagier
• The Euler characteristic of the moduli space of curves
• Some combinatorial problems associated with products of conjugacy classes of the symmetric group
• Counting trees using symmetries
• A direct bijection for the Harer-Zagier formula
• Démonstration combinatoire de la formule de Harer–Zagier
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