Pascal arrays: counting Catalan sets
Bethany Marsh, Paul Martin
TL;DR
This paper explores the internal structure of Catalan sequences and their generalizations, revealing connections to known mathematical structures and introducing new ones, motivated by representation theory.
Contribution
It uncovers an interior structure of Catalan sequences, linking some to known structures and proposing new generalizations, advancing understanding in combinatorics and representation theory.
Findings
Identification of an interior structure within Catalan sequences
Connection of some structures to well-known mathematical entities
Introduction of new generalizations of Catalan sequences
Abstract
Motivated by representation theory we exhibit an interior structure to Catalan sequences and many generalisations thereof. Certain of these coincide with well known (but heretofore isolated) structures. The remainder are new.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · semigroups and automata theory