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Graphs and Combinatorics

, Volume 35, Issue 1, pp 169–187 | Cite as

Bijections of Motzkin Paths Using Shifted Riordan Decompositions

  • Aoife HennessyEmail author
Original Paper
  • 49 Downloads

Abstract

This paper concerns bijections between Motzkin and Łukasiewicz paths arising from Riordan array decompositions. Bijections have been shown between Motzkin paths and Łukasiewicz paths with constant weights (Hennessy in A study of riordan srrays with applications to continued fractions, orthogonal polynomials and lattice paths. Ph.D. thesis, Waterford Institute of Technology, 2011). We introduce a shifting matrix technique to induce a bijection between Motzkin paths and Łukasiewicz paths with non constant weighted steps. We will show a generating function proof and a construction of these bijections.

Keywords

Riordan array Motzkin path Łukasiewicz path 

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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Waterford Institute of TechnologyWaterfordRepublic of Ireland

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