Bi-banded paths, a bijection and the Narayana numbers

Judy Anne Osborn

Bi-banded paths, a bijection and the Narayana numbers

Judy Anne Osborn^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We find a bijection between bi-banded paths and peak-counting paths, applying to two classes of lattice paths including Dyck paths. Thus we find a new interpretation of Narayana numbers as coefficients of weight polynomials enumerating bi-banded Dyck paths, which class of paths has arisen naturally in previous literature in a solution of the stationary state of the 'TASEP' stochastic process.

Original language	English
Pages (from-to)	243-252
Number of pages	10
Journal	Australasian Journal of Combinatorics
Volume	48
Publication status	Published - Oct 2010

Cite this

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abstract = "We find a bijection between bi-banded paths and peak-counting paths, applying to two classes of lattice paths including Dyck paths. Thus we find a new interpretation of Narayana numbers as coefficients of weight polynomials enumerating bi-banded Dyck paths, which class of paths has arisen naturally in previous literature in a solution of the stationary state of the 'TASEP' stochastic process.",

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AB - We find a bijection between bi-banded paths and peak-counting paths, applying to two classes of lattice paths including Dyck paths. Thus we find a new interpretation of Narayana numbers as coefficients of weight polynomials enumerating bi-banded Dyck paths, which class of paths has arisen naturally in previous literature in a solution of the stationary state of the 'TASEP' stochastic process.

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Bi-banded paths, a bijection and the Narayana numbers

Abstract

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