10 citations · 15 across the 4 of their papers we have counts for
4 papers
Contents of partitions and the combinatorics of permutation factorizations in genus 0
S. R. Carrell, I. P. Goulden
The central object of study is a formal power series that we call the content series, a symmetric function involving an arbitrary underlying formal power series in the contents…
Hook Weighted Increasing Trees, Cayley Trees and Abel-Hurwitz Identities
S. R. Carrell
Recently Féray, Goulden and Lascoux gave a proof of a new hook summation formula for unordered increasing trees by means of a generalization of the Prüfer code for labelled trees a…
The Non-Orientable Map Asymptotics Constant
S. R. Carrell
Using the pfaffian structure of the generating series for locally orientable maps, we show that the generating series satsifies a nonlinear differential equation called the BKP equ…
Simple recurrence formulas to count maps on orientable surfaces
Sean R. Carrell, Guillaume Chapuy
We establish a simple recurrence formula for the number of rooted orientable maps counted by edges and genus. We also give a weighted variant for the generating polynomial…