5 papers
Tournament score sequences, Erdős-Ginzburg-Ziv numbers, and the Lévy-Khintchine method
Michal Bassan, Serte Donderwinkel, Brett Kolesnik
We give a short proof of a recent result of Claesson, Dukes, Franklín and Stefánsson, connecting the number of score sequences and the Erdős-Ginzburg-Ziv numbers from a…
Graphical sequences and plane trees
Michal Bassan, Serte Donderwinkel, Brett Kolesnik
Balister, the second author, Groenland, Johnston and Scott recently showed that there are asymptotically many unordered sequences that occur as degree sequences of g…
Critical beta-splitting, via contraction
Brett Kolesnik
The critical beta-splitting tree, introduced by Aldous, is a Markov branching phylogenetic tree. Aldous and Pittel recently proved, amongst other results, a central limit theorem f…
Sinaĭ excursions: An analogue of Sparre Andersen's formula for the area process of a random walk
Serte Donderwinkel, Brett Kolesnik
Sinaĭ initiated the study of random walks with persistently positive area processes, motivated by shock waves in solutions to the inviscid Burgers' equation. We find the precise as…
Tournaments and random walks
Serte Donderwinkel, Brett Kolesnik
We study the relationship between tournaments and random walks. This connection was first observed by Erdős and Moser. Winston and Kleitman came close to showing that $S_n=Θ(4^n/n^…