Down-step statistics in generalized Dyck paths
نویسندگان
چکیده
The number of down-steps between pairs up-steps in $k_t$-Dyck paths, a generalization Dyck paths consisting steps $\{(1, k), (1, -1)\}$ such that the path stays (weakly) above line $y=-t$, is studied. Results are proved bijectively and by means generating functions, lead to several interesting identities as well links other combinatorial structures. In particular, there connection perforation patterns for punctured convolutional codes (binary matrices) used coding theory. Surprisingly, upon restriction usual this yields new interpretation Catalan numbers.
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ژورنال
عنوان ژورنال: Discrete Mathematics & Theoretical Computer Science
سال: 2022
ISSN: ['1365-8050', '1462-7264']
DOI: https://doi.org/10.46298/dmtcs.7163