Pascal arrays: counting Catalan sets

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.

55 pages, 28 figures, the source file is catalan4.tex

References in corpus (3)

• Local limit of labeled trees and expected volume growth in a random quadrangulation
• The blocks of the Brauer algebra in characteristic zero
• Cuntz-Krieger algebras and a generalization of Catalan numbers

Cited by in corpus (2)

• Tiling bijections between paths and Brauer diagrams
• On geometrically defined extensions of the Temperley-Lieb category in the Brauer category