Pavel Turek

activity

20232026

collaborators

9 papers

math.RT2026

New columns in decomposition matrices of symmetric groups for every block

David J. Hemmer, Pavel Turek

The central unsolved problem in the modular representation theory of symmetric groups is to find the decomposition matrices, which describe how irreducible representations in chara…

math.CO2026

Divisible Arm Lengths, Crystal Reflections, and Enumeration of Newly Found Decomposition Columns

David J. Hemmer, Pavel Turek

In recent work the authors determine complete columns of symmetric-group decomposition matrices in odd prime characteristic $p$ labeled by $p$ -regular partitions for which every ho…

math.RT2025

Symmetric powers of $S^{(n - 1, 1)}$ and $D^{(n - 1, 1)}$

Pavel Turek, Jialin Wang

Let $p$ be a prime and $n \geq 2$ be a positive integer. We establish new formulae for the decompositions of the first $p - 1$ symmetric powers of the Specht module $S^{(n - 1, 1)}$ and…

math.CO2025

Mullineux map: $d$ -balanced partitions and $d$ -runner matrices

Pavel Turek

Let $d, e > 1$ be two integers. For $e$ prime, the Mullineux map $m_{e}$ describes tensor products of the irreducible modules of symmetric groups with the sign in characteristic $e$ as…

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…

math.CO2024

Towards odd-sunflowers: temperate families and lightnings

Jan Petr, Pavel Turek

Motivated by odd-sunflowers, introduced recently by Frankl, Pach, and P{á}lv{ö}lgyi, we initiate the study of temperate families: a family $F \subseteq P ([n])$ …

math.CO2023

Proof of the plethystic Murnaghan-Nakayama rule using Loehr's labelled abacus

Pavel Turek

The plethystic Murnaghan-Nakayama rule describes how to decompose the product of a Schur function and a plethysm of the form $p_{r} \circ h_{m}$ as a sum of Schur functions. We provide…

math.RT2023

Multiplicity-free induced characters of symmetric groups

Pavel Turek

Let $n$ be a non-negative integer. Combining algebraic and combinatorial techniques, we investigate for which pairs $(G, ρ)$ of a subgroup $G$ of the symmetric group $S_{n}$ and an ir…

New columns in decomposition matrices of symmetric groups for every block

Divisible Arm Lengths, Crystal Reflections, and Enumeration of Newly Found Decomposition Columns

Symmetric powers of S(n−1,1) and D(n−1,1)

Mullineux map: d-balanced partitions and d-runner matrices

Intervals in Dyck paths and the wreath conjecture

The wreath matrix

Towards odd-sunflowers: temperate families and lightnings

Proof of the plethystic Murnaghan-Nakayama rule using Loehr's labelled abacus

Multiplicity-free induced characters of symmetric groups

Symmetric powers of $S^{(n - 1, 1)}$ and $D^{(n - 1, 1)}$

Mullineux map: $d$ -balanced partitions and $d$ -runner matrices