Combinatorial proofs of addition formulas
type: Item
instance of: scholarly article
title: Combinatorial proofs of addition formulas
zbMATH Open document ID: 1329.05027
author: Xiangke Chang
author: Xing-Biao Hu
author: Hongchuan Lei
author: Yeong-Nan Yeh
published in: The Electronic Journal of Combinatorics
publication date: 2016-01-25T00:00:00Z
full work available at URL: v23i1p8
review text: Summary: In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the \(LDU\) decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition formula for weighted large Schröder paths.
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 6534991
zbMATH Keywords: lattice paths
zbMATH Keywords: Catalan numbers
zbMATH Keywords: Motzkin numbers
zbMATH Keywords: large Schröder numbers
zbMATH Keywords: Hankel determinant
describes a project that uses: OEIS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6534991