3 papers
math.CO2022
The maximum hook length of -distinct simultaneous core partitions
Ethan Pesikoff, Benjamin Przybocki, Janabel Xia
We exactly determine the maximum possible hook length of -core partitions with -distinct parts when there are finitely many such partitions. Moreover, we provide an algor…
math.CO2021
Lengths of Irreducible and Delicate Words
Benjamin Przybocki
We study words that barely avoid repetitions, for several senses of "barely". A squarefree (respectively, overlap-free, cubefree) word is irreducible if removing any one of its int…
math.CO2020
Hat Guessing on Books and Windmills
Xiaoyu He, Yuzu Ido, Benjamin Przybocki
The hat-guessing number is a graph invariant defined by Butler, Hajiaghayi, Kleinberg, and Leighton. We determine the hat-guessing number exactly for book graphs with sufficiently…