We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.
Bibliographical noteFunding Information:
The authors would like to thank the anonymous referees for carefully reading the paper and giving helpful comments and suggestions. The second author was partially supported by Universidad Nacional de Colombia, Project No. 46240.
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.
- Catalan word
- Generating function
- Interior points
- Vertex degree
ASJC Scopus subject areas
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics