Jacobsthal decompositions of pascal’s triangle, ternary trees, and alternating sign matrices

Barry, Paul (2016) Jacobsthal decompositions of pascal’s triangle, ternary trees, and alternating sign matrices. Journal of Integer Sequences, 19 (3). ISSN 1530-7638

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Abstract

We examine Jacobsthal decompositions of Pascal’s triangle and Pascal’s square from a number of points of view, making use of bivariate generating functions, which we de-rive from a truncation of the continued fraction generating function of the Narayana number triangle. We establish links with Riordan array embedding structures. We explore determinantal links to the counting of alternating sign matrices and plane partitions and sequences related to ternary trees. Finally, we examine further relationships between bivariate generating functions, Riordan arrays, and interesting number squares and triangles.

Item Type:	Article
Additional Information:	Publisher Copyright: © 2016, University of Waterloo. All Right Reserved.
Uncontrolled Keywords:	/dk/atira/pure/subjectarea/asjc/2600/2607
Departments or Groups:
Depositing User:	Admin SSL
Date Deposited:	19 Oct 2022 23:05
Last Modified:	02 Feb 2023 00:01
URI:	http://repository-testing.wit.ie/id/eprint/3940

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