Combinatorial proofs of addition formulas (Q907256)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Combinatorial proofs of addition formulas |
scientific article; zbMATH DE number 6534991
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Combinatorial proofs of addition formulas |
scientific article; zbMATH DE number 6534991 |
Statements
Combinatorial proofs of addition formulas (English)
0 references
25 January 2016
0 references
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.
0 references
lattice paths
0 references
Catalan numbers
0 references
Motzkin numbers
0 references
large Schröder numbers
0 references
Hankel determinant
0 references
0 references
