DeepAI AI Chat
Log In Sign Up

Dyck paths with catastrophes modulo the positions of a given pattern

by   Jean-Luc Baril, et al.
Université de Bourgogne

For any pattern p of length at most two, we provide generating functions and asymptotic approximations for the number of p-equivalence classes of Dyck paths with catastrophes, where two paths of the same length are p-equivalent whenever the positions of the occurrences of the pattern p are the same.


page 1

page 2

page 3

page 4


Popularity of patterns over d-equivalence classes of words and permutations

Two same length words are d-equivalent if they have same descent set and...

Pattern statistics in faro words and permutations

We study the distribution and the popularity of some patterns in words o...

Bijections from Dyck and Motzkin meanders with catastrophes to pattern avoiding Dyck paths

In this note, we present constructive bijections from Dyck and Motzkin m...

Lattice paths with a first return decomposition constrained by the maximal height of a pattern

We consider the system of equations A_k(x)=p(x)A_k-1(x)(q(x)+∑_i=0^k A_i...

Prolific Compositions

Under what circumstances might every extension of a combinatorial struct...

Enumeration of Dyck paths with air pockets

We introduce and study the new combinatorial class of Dyck paths with ai...

Ocular dominance patterns in mammalian visual cortex: A wire length minimization approach

We propose a theory for ocular dominance (OD) patterns in mammalian prim...