English

k-non-crossing trees and edge statistics modulo k

Combinatorics 2024-03-22 v1

Abstract

Instead of kk-Dyck paths we consider the equivalent concept of kk-non-crossing trees. This is our preferred approach relative to down-step statistics modulo kk (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.

Keywords

Cite

@article{arxiv.2403.13937,
  title  = {k-non-crossing trees and edge statistics modulo k},
  author = {Helmut Prodinger},
  journal= {arXiv preprint arXiv:2403.13937},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-28T15:27:55.606Z