6 papers · 1 filter
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 labeled by -regular partitions for which every ho…
Mullineux map: -balanced partitions and -runner matrices
Pavel Turek
Let be two integers. For prime, the Mullineux map describes tensor products of the irreducible modules of symmetric groups with the sign in characteristic as…
Intervals in Dyck paths and the wreath conjecture
Jan Petr, Pavel Turek
Let denote the total number of intervals of length across all Dyck paths of semilength such that each interval contains precisely falls. We give the formul…
The wreath matrix
Jan Petr, Pavel Turek
Let be positive integers and be the set of integers modulo . A conjecture of Baranyai from 1974 asks for a decomposition of -element subsets of $\m…
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 …
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 as a sum of Schur functions. We provide…