Jan Petr

collaborators

3 papers

math.CO2026

Ordered Ramsey and Turán numbers of alternating paths and their variants

Gaurav Kucheriya, Allan Lo, Jan Petr +2

An ordered graph is a graph whose vertex set is equipped with a total order. The ordered complete graph $K_{N}^{<}$ is the complete graph with vertex set $[N]$ equipped with the natura…

math.CO2025

Intervals in Dyck paths and the wreath conjecture

Jan Petr, Pavel Turek

Let $ι_{k} (m, l)$ denote the total number of intervals of length $m$ across all Dyck paths of semilength $k$ such that each interval contains precisely $l$ falls. We give the formul…

math.CO2025

The wreath matrix

Jan Petr, Pavel Turek

Let $k \leq n$ be positive integers and $Z_{n}$ be the set of integers modulo $n$ . A conjecture of Baranyai from 1974 asks for a decomposition of $k$ -element subsets of $\m…