Jan Petr

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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…