10 citations · 16 across the 6 of their papers we have counts for
6 papers · 1 filter
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…
Diagonal Solutions to the 2-Toda Hierarchy
S. R. Carrell
Using a combinatorial description of the Bernstein operator and its action on Schur functions, we describe the formal power series solutions to a family of partial differential equ…
Symmetric functions, codes of partitions and the KP hierarchy
S. R. Carrell, I. P. Goulden
We consider an operator of Bernstein for symmetric functions, and give an explicit formula for its action on an arbitrary Schur function. This formula is given in a remarkably simp…