Transitive factorizations of permutations and geometry

2014/07/28 by I. P. Goulden, D. M. Jackson, Goulden, I. P. +1
Engineering · Mathematics · #05E05 #14N35 #15B52 #57M12 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary 05A15 #Secondary 05C10 #graph theory and CDMA systems #math.AG #math.CO #msc:05A15 #msc:05C10 #msc:05E05 #msc:14N35 #msc:15B52 #msc:57M12

paper · pdf · doi:10.48550/arxiv.1407.7568

12 pages, dedicated to Richard Stanley on the occasion of his 70th birthday

arxiv created 2014/07/28 · openalex publication_date 2014/07/28 · arxiv updated 2014/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves. Aspects of these seemingly unrelated areas are seen to be related in a unifying view from the perspective of algebraic combinatorics. At several points this work has intertwined with Richard Stanley's in significant ways.

Related

• Minimal transitive factorizations of permutations into cycles
• Minimal Transitive Factorizations of Permutations into Cycles
• Bijections and symmetries for the factorizations of the long cycle
• Transitive factorisations in the symmetric group, and combinatorial aspects of singularity theory
• Inequivalent Factorizations of Permutations