paper

k-non-crossing trees and edge statistics modulo k

arXiv:2403.13937

Abstract

Instead of -Dyck paths we consider the equivalent concept of -non-crossing trees. This is our preferred approach relative to down-step statistics modulo (first studied by Heuberger, Selkirk, and Wagner by different methods). One symmetry argument about subtrees is needed and the rest goes along the lines of a paper by Flajolet and Noy.

Early and rough version; completed while in Graz, Austria. Comments are VERY welcome

k-non-crossing trees and edge statistics modulo k · wovepaper