The Pascal Rhombus and the Generalized Grand Motzkin Paths
Jos\'e L. Ram\'irez
TL;DR
This paper derives a closed-form formula for the Pascal rhombus entries and explores their connection to generalized grand Motzkin paths, revealing new combinatorial relationships.
Contribution
It introduces a closed expression for Pascal rhombus entries and links them to a new family of generalized grand Motzkin paths.
Findings
Closed-form expression for Pascal rhombus entries
Established relation between Pascal rhombus and generalized grand Motzkin paths
New combinatorial identities involving these structures
Abstract
In the present article, we find a closed expression for the entries of the Pascal rhombus. Moreover, we show a relation between the entries of the Pascal rhombus and a family of generalized grand Motzkin paths.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · semigroups and automata theory