Geodesic
Enumerating symmetric peaks in non-decreasing Dyck paths
Ars Mathematica Contemporanea, Tome 21 (2021) no. 2, article no. 04, 23 p.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

Local maxima and minima of a Dyck path are called peaks and valleys, respectively. A Dyck path is non-decreasing if the heights (y-coordinates) of its valleys increase from left to right. A peak is symmetric if it is surrounded by two valleys (or endpoints of the path) at the same height. In this paper we give multivariate generating functions, recurrence relations, and closed formulas to count the number of symmetric and asymmetric peaks in non-decreasing Dyck paths. Finally, we use Riordan arrays to study weakly symmetric peaks, namely those for which the valley preceding the peak is at least as high as the valley following it.
DOI : 10.26493/1855-3974.2478.d1b
Keywords: Non-decreasing Dyck path, symmetric peak, generating function, Riordan array, Fibonacci number 
@article{10_26493_1855_3974_2478_d1b,
     author = {Sergi Elizalde and Rigoberto Fl\'orez and Jos\'e Luis Ram{\'\i}rez},
     title = {Enumerating symmetric peaks in non-decreasing {Dyck} paths},
     journal = {Ars Mathematica Contemporanea},
     eid = {04},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2021},
     doi = {10.26493/1855-3974.2478.d1b},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2478.d1b/}
}
TY  - JOUR
AU  - Sergi Elizalde
AU  - Rigoberto Flórez
AU  - José Luis Ramírez
TI  - Enumerating symmetric peaks in non-decreasing Dyck paths
JO  - Ars Mathematica Contemporanea
PY  - 2021
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2478.d1b/
DO  - 10.26493/1855-3974.2478.d1b
LA  - en
ID  - 10_26493_1855_3974_2478_d1b
ER  - 
%0 Journal Article
%A Sergi Elizalde
%A Rigoberto Flórez
%A José Luis Ramírez
%T Enumerating symmetric peaks in non-decreasing Dyck paths
%J Ars Mathematica Contemporanea
%D 2021
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2478.d1b/
%R 10.26493/1855-3974.2478.d1b
%G en
%F 10_26493_1855_3974_2478_d1b
Sergi Elizalde; Rigoberto Flórez; José Luis Ramírez. Enumerating symmetric peaks in non-decreasing Dyck paths. Ars Mathematica Contemporanea, Tome 21 (2021) no. 2, article  no. 04, 23 p. doi : 10.26493/1855-3974.2478.d1b. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2478.d1b/

Cité par Sources :