May 28, 2008 · Title:Potential Polynomials and Motzkin Paths ... Abstract: A {\em Motzkin path} of length n is a lattice path from (0,0) to (n,0) in the plane ...
The present paper studies two kinds of statistics on Motzkin paths: “number of u -segments” and “number of h -segments”.
Apr 21, 2015 · Recall that a Motzkin path consists of a sequence of steps with each step being one of three possible types: up, down or horizontal. Now, to ...
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Oct 22, 2024 · Associated with the Motzkin paths, we introduce the Motzkin polynomial, which is a multi-variable polynomial “counting” all Motzkin paths of a ...
Dec 5, 2017 · The number of paths of length n with k up step is given by the Motzkin polynomial coefficient Tn,k. First let us define a lattice path. A ...
Apr 21, 2015 · We consider the Motzkin paths which are simple combinatorial objects appearing in many contexts. They are counted by the Motzkin numbers, related to the well ...
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Feb 6, 2024 · Motzkin) paths with suitable weights for each rise and fall (resp. ... possible inversion tables. Given the inversion table p, we can ...
Jul 29, 2015 · Abstract. We study the moments of orthogonal polynomial sequences (OPS) arising from tridiagonal matrices.
Oct 6, 2011 · This theory tells us, that the moments of any family of orthogonal polynomials are given by a certain weighted count of Motzkin paths.
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A Motzkin path of length n is lattice path in the plane from (0,0) to (n,0) consisting of up steps U = (1,1), down steps D = (1,−1) and horizontal steps H = (1, ...
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