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…
An edge-weighted hook formula for labelled trees
Valentin Féray, I. P. Goulden, A. Lascoux
A number of hook formulas and hook summation formulas have previously appeared, involving various classes of trees. One of these classes of trees is rooted trees with labelled vert…
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…
Transitive factorisations in the symmetric group, and combinatorial aspects of singularity theory
I. P. Goulden, D. M. Jackson
We consider the determination of the number of ordered factorisations of an arbitrary permutation on n symbols, with cycle distribution , into k-cycles such that the fa…