1. On doubly symmetric Dyck words
- Author
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Andrea Frosini, Robert Cori, Elisa Pergola, Giulia Palma, and Simone Rinaldi
- Subjects
Sequence ,Mathematics::Combinatorics ,Symmetry operation ,General Computer Science ,Computation ,Integer sequence ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Enumerative combinatorics ,Theoretical Computer Science ,Combinatorics ,Recursive algorithms ,Representation (mathematics) ,Bijection, injection and surjection ,Computer Science::Formal Languages and Automata Theory ,Mathematics - Abstract
In this paper we consider doubly symmetric Dyck words, i.e. Dyck words which are fixed by two symmetry operations α and β introduced in [1] . We study combinatorial properties of doubly symmetric Dyck words, leading to the definition of two recursive algorithms to build these words. As a consequence we have a representation of doubly symmetric Dyck words as vectors of integers, called track vectors. Finally, we show some bijections between a subfamily of doubly symmetric Dyck words and a subfamily of integer partitions. The computation of the sequence f n of doubly symmetric Dyck words of semi-length n shows surprising properties giving rise to some conjectures.
- Published
- 2021