| Issue |
RAIRO-Theor. Inf. Appl.
Volume 58, 2024
|
|
|---|---|---|
| Article Number | 1 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/ita/2024001 | |
| Published online | 15 February 2024 | |
Consecutive pattern-avoidance in Catalan words according to the last symbol
1
LIB, Université de Bourgogne,
BP 47 870,
21078
Dijon-Cedex
France.
2
Departamento de Matemáticas, Universidad Nacional de Colombia,
Bogotá,
Colombia.
* Corresponding author: jlramirezr@unal.edu.co
Received:
3
February
2023
Accepted:
11
January
2024
We study the distribution of the last symbol statistics on the sets of Catalan words avoiding a consecutive pattern of length at most three. For each pattern p, we provide a bivariate generating function, where the coefficient cp(n,k) of xnyk in its series expansion is the number of length n Catalan words avoiding p and ending with the symbol k. We deduce recurrence relations or closed forms for cp(n, k) and we provide asymptotic approximations for the expectation of the last symbol on all Catalan words avoiding p. Finally, we characterize the sequence cp(n, k) using Riordan arrays.
Mathematics Subject Classification: 05A15 / 05A19
Key words: Catalan word / consecutive pattern / generating function
© The authors. Published by EDP Sciences, 2024
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