1. On doubly symmetric Dyck words.
- Author
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Cori, Robert, Frosini, Andrea, Palma, Giulia, Pergola, Elisa, and Rinaldi, Simone
- Subjects
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VOCABULARY , *INTEGERS , *SYMMETRY , *ALGORITHMS , *LOGICAL prediction - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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