6 papers · 1 filter
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 is the species of interval orders a…
Inversion monotonicity in subclasses of the 1324-avoiders
Anders Claesson, Svante Linusson, Henning Ulfarsson +1
A collection of patterns is called inversion monotone if , the number of -avoiding permutations of length with inversions, is weakly increasing i…
Counting fixed-point-free Cayley permutations
Giulio Cerbai, Anders Claesson
Two-sort species yield differential equations for functional digraphs of Cayley permutations. From these we obtain an explicit formula for fixed-point-free Cayley permutations and…
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…
Modified difference ascent sequences and Fishburn structures
Giulio Cerbai, Anders Claesson, Bruce Sagan
Ascent sequences and their modified version play a central role in the bijective framework relating several combinatorial structures counted by the Fishburn numbers. Ascent sequenc…
Self-modified difference ascent sequences
Giulio Cerbai, Anders Claesson, Bruce E. Sagan
Ascent sequences play a key role in the combinatorics of Fishburn structures. Difference ascent sequences are a natural generalization obtained by replacing ascents with -ascent…