Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem

Abstract

In this paper we construct a bijection for partitioned 3-cacti that gives raise to a new formula for enumeration of factorizations of the long cycle into three permutations with given number of cycles.

Keywords

• harer-zagier formula
• jackson formula
• cactus trees
• cacti
• permutations
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]