7 papers
The mex statistic on combinatorial structures
Antonio Bernini, Stefano Bilotta, Giulio Cerbai +1
We extend the notion of mex, which is central in combinatorial number theory, to an arbitrary combinatorial structure, and we prove a general theorem to determine the generating fu…
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…
Pattern-avoiding modified ascent sequences
Giulio Cerbai
We initiate an in-depth study of pattern avoidance on modified ascent sequences. Our main technique consists in using Stanley's standardization to obtain a transport theorem betwee…