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

Paul Barry

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number16.3.5
JournalJournal of Integer Sequences
Volume19
Issue number3
Publication statusPublished - 06 Apr 2016

Keywords

  • Alternating sign matrix
  • Binomial matrix
  • Jacobsthal number
  • Pascal’s triangle
  • Plane partition
  • Riordan array
  • Ternary tree

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