3 papers
math.CO2026
Cyclomatic numbers and permutations
Bridget Eileen Tenner, Vincent Vatter
We show that several apparently different aspects of a permutation are all tied to a single quantity, the cyclomatic number of its inversion graph. Every reduced word for the permu…
math.CO2026
Boolean--Eulerian numbers
Miklós Bóna, Vincent Vatter
We study decreasing binary trees in which every vertex with two children is colored red or blue. We construct two bijections. The first, to ordered set partitions into odd-sized bl…
math.CO2025
Uncountably many enumerations of well-quasi-ordered permutation classes
Robert Brignall, Vincent Vatter
We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a conjecture that all well-quasi-ordered per…