11 citations · 12 across the 17 of their papers we have counts for
21 papers
Finiteness theorems for Cayley permutation classes
Giulio Cerbai, Anders Claesson
We prove that every hereditary Cayley permutation class with finitely many simple members has a finite basis and an algebraic generating function. We first show that every simple C…
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…
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 Cayley permutations via combinatorial species
Anders Claesson, Giulio Cerbai, Dana C. Ernst +1
A Cayley permutation is a word of positive integers such that if a letter appears in this word, then all positive integers smaller than that letter also appear. We initiate a syste…
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…
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…
Caylerian polynomials
Giulio Cerbai, Anders Claesson
The Eulerian polynomials enumerate permutations according to their number of descents. We initiate the study of descent polynomials over Cayley permutations, which we call Cayleria…
On a conjecture on pattern-avoiding machines
Christopher Bao, Giulio Cerbai, Yunseo Choi +2
Let be West's stack-sorting map, and let be the generalized stack-sorting map, where instead of being required to increase, the stack avoids subpermutations that are or…
Modified ascent sequences and Bell numbers
Giulio Cerbai
In 2011, Duncan and Steingrímsson conjectured that modified ascent sequences avoiding any of the patterns 212, 1212, 2132, 2213, 2231 and 2321 are counted by the Bell numbers. Furt…
Fishburn trees
Giulio Cerbai, Anders Claesson
The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the verte…
Sorting permutations with pattern-avoiding machines
Giulio Cerbai
In this work of thesis we introduce and study a new family of sorting devices, which we call pattern-avoiding machines. They consist of two stacks in series, equipped with a greedy…
Dynamical aspects of -machines
Giulio Cerbai
The -machine was recently introduced by Cerbai, Claesson and Ferrari as a tool to gain a better insight on the problem of sorting permutations with two stacks in series. It cons…
Sorting with pattern-avoiding stacks: the -machine
Giulio Cerbai, Anders Claesson, Luca Ferrari +1
This paper continues the analysis of the pattern-avoiding sorting machines recently introduced by Cerbai, Claesson and Ferrari [CCF]. These devices consist of two stacks, through w…
Transport of patterns by Burge transpose
Giulio Cerbai, Anders Claesson
We take the first steps in developing a theory of transport of patterns from Fishburn permutations to (modified) ascent sequences. Given a set of pattern avoiding Fishburn permutat…
Sorting Cayley permutations with pattern-avoiding machines
Giulio Cerbai
Pattern avoiding machines were recently introduced by Claesson, Ferrari and the current author to gain a better understanding of the classical -stacksort problem. In this paper…
Stack Sorting with Increasing and Decreasing Stacks
Giulio Cerbai, Lapo Cioni, Luca Ferrari
We introduce a sorting machine consisting of stacks in series: the first stacks can only contain elements in decreasing order from top to bottom, while the last one has t…
Stack sorting with restricted stacks
Giulio Cerbai, Anders Claesson, Luca Ferrari
The (classical) problem of characterizing and enumerating permutations that can be sorted using two stacks connected in series is still largely open. In the present paper we addres…
Permutation patterns in genome rearrangement problems: the reversal model
Giulio Cerbai, Luca Ferrari
In the context of the genome rearrangement problem, we analyze two well known models, namely the reversal and the prefix reversal models, by exploiting the connection with the noti…
Permutation patterns in genome rearrangement problems
Giulio Cerbai, Luca Ferrari
In the context of the genome rearrangement problem, we analyze two well known models, namely the block transposition and the prefix block transposition models, by exploiting the co…