4 papers
Tree-indexed sums of Catalan numbers
Alin Bostan, Valentin Féray, Paul Thévenin
We consider a family of infinite sums of products of Catalan numbers, indexed by trees. We show that these sums are polynomials in with rational coefficients; the proof is ef…
Existence of critical tiltings and local limits of general size-conditioned Bienaymé-Galton-Watson multitype trees
Rémy Poudevigne, Paul Thévenin
We are interested in the structure of multitype Bienaymé-Galton-Watson (BGW) trees conditioned on integer linear combinations of the numbers of vertices of given types. We show tha…
Sharp character bounds and cutoff for symmetric groups
Sam Olesker-Taylor, Lucas Teyssier, Paul Thévenin
We develop a flexible technique to bound the characters of symmetric groups, via the Naruse hook length formula, the Larsen--Shalev character bounds, and appropriate diagram slicin…
Characters of symmetric groups: sharp bounds on virtual degrees and the Witten zeta function
Lucas Teyssier, Paul Thévenin
We prove sharp bounds on the virtual degrees introduced by Larsen and Shalev. This leads to improved bounds on characters of symmetric groups. We then sharpen bounds of Liebeck and…