Another proof of the Harer-Zagier formula

zbMath1330.05017arXiv1503.05598MaRDI QIDQ2635085

Boris G. Pittel

Publication date: 11 February 2016

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.05598

zbMATH Keywords

Fourier transformgenerating functionsirreducible characterssurfacesgenusrandom permutationschord diagramsMurnaghan-Nakayama

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of representation theory (05E10) Asymptotic enumeration (05A16) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Probabilistic methods in group theory (20P05)

Related Items (4)

Formation of a giant component in the intersection graph of a random chord diagram ⋮ Calculating the Euler characteristic of the moduli space of curves ⋮ On generalizations of Chebyshev polynomials and Catalan numbers ⋮ Generalisations of the Harer-Zagier recursion for 1-point functions

Cites Work

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• The Euler characteristic of the moduli space of curves
• Two enumerative results on cycles of permutations
• Démonstration combinatoire de la formule de Harer–Zagier
• Large deviations and moments for the Euler characteristic of a random surface
• Counting Cycles in Permutations by Group Characters, With an Application to a Topological Problem
• Generating a random permutation with random transpositions
• Topological characteristics of random triangulated surfaces

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