A bijective proof of Jackson's formula for the number of factorizations of a cycle

DOI10.1016/j.jcta.2007.12.002zbMath1155.05007OpenAlexW1999660929WikidataQ114162750 ScholiaQ114162750MaRDI QIDQ941309

Gilles Schaeffer, Ekaterina A. Vassilieva

Publication date: 4 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.jcta.2007.12.002

zbMATH Keywords

permutationssymmetric groupfactorizationsEulerian toursbicolored treesHarer-Zagier Formulaunicellular bicolored maps

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05)

Related Items (20)

On the matchings-Jack conjecture for Jack connection coefficients indexed by two single part partitions ⋮ A combinatorial way of counting unicellular maps and constellations ⋮ Unnamed Item ⋮ A simple model of trees for unicellular maps ⋮ Bijective enumeration of 3-factorizations of an \(N\)-cycle ⋮ Bijections and symmetries for the factorizations of the long cycle ⋮ Moments of normally distributed random matrices given by generating series for connection coefficients -- explicit bijective computation ⋮ Calculating the Euler characteristic of the moduli space of curves ⋮ Direct bijective computation of the generating series for 2 and 3-connection coefficients of the symmetric group ⋮ An analogue of the Harer-Zagier formula for unicellular maps on general surfaces ⋮ Bijective enumeration of some colored permutations given by the product of two long cycles ⋮ Separation Probabilities for Products of Permutations ⋮ A bijection for covered maps, or a shortcut between Harer-Zagiers and Jacksons formulas ⋮ A new combinatorial identity for unicellular maps, via a direct bijective approach ⋮ \(\operatorname{GL}_n(\mathbb{F}_q)\)-analogues of factorization problems in the symmetric group ⋮ Unnamed Item ⋮ Some formulas for the number of gluings ⋮ Factorization problems in complex reflection groups ⋮ 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

• An analog of the Harer-Zagier formula for unicellular bicolored maps
• Factoring \(n\)-cycles and counting maps of given genus
• Graphs on surfaces and their applications. Appendix by Don B. Zagier
• Maps, hypermaps and their automorphisms: A survey. III
• The Euler characteristic of the moduli space of curves
• Some combinatorial problems associated with products of conjugacy classes of the symmetric group
• Counting rooted maps by genus. I
• A direct bijection for the Harer-Zagier formula
• Démonstration combinatoire de la formule de Harer–Zagier
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A bijective proof of Jackson's formula for the number of factorizations of a cycle