Anders Claesson

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math.CO2026

The species of interval orders

Anders Claesson

We show that, in the ring of virtual species, \[ \mathcal{I}=\sum_{m\geq 0}(-1)^m\prod_{i=1}^{m}\bigl((E^{-1})^i-1\bigr), \] where $I$ is the species of interval orders a…

math.CO2026

Inversion monotonicity in subclasses of the 1324-avoiders

Anders Claesson, Svante Linusson, Henning Ulfarsson +1

A collection $B$ of patterns is called inversion monotone if $av_{n}^{k} (B)$ , the number of $B$ -avoiding permutations of length $n$ with $k$ inversions, is weakly increasing i…

math.CO2024

Enumerative aspects of Caylerian polynomials

Giulio Cerbai, Anders Claesson

Eulerian polynomials record the distribution of descents over permutations. Caylerian polynomials likewise record the distribution of descents over Cayley permutations, where a Cay…