Determinant identities for the Catalan, Motzkin and Schröder numbers

DOI10.26493/2590-9770.1645.d36MaRDI QIDQ6087086

T. P. Goy, Mark Shattuck

Publication date: 11 December 2023

Published in: The Art of Discrete and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Catalan numberMotzkin numberlattice pathHessenberg matrixSchröder numbercombinatorial proofgeneralized Trudi's formula

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Matrices, determinants in number theory (11C20) Toeplitz, Cauchy, and related matrices (15B05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A unified approach for the Hankel determinants of classical combinatorial numbers
• Identities involving weighted Catalan, Schröder and Motzkin paths
• Hankel determinants of sums of consecutive Motzkin numbers
• Some identities on the Catalan, Motzkin and Schröder numbers
• Identities involving Narayana polynomials and Catalan numbers
• Bijective recurrences concerning Schröder paths
• Dyck path enumeration
• A note on the determinant of a Toeplitz-Hessenberg matrix
• Hankel determinants of shifted Catalan-like numbers
• Determinant formulas of some Toeplitz-Hessenberg matrices with Catalan entries
• Determinant identities for toeplitz-hessenberg matrices with tribonacci entries
• Catalan Numbers
• Motzkin numbers of higher rank: Generating function and explicit expression
• Permanents, Determinants, Weighted Isobaric Polynomials and Integer Sequences
• Motzkin numbers
• Motzkin numbers
• s-Catalan numbers and Littlewood-Richardson polynomials

This page was built for publication: Determinant identities for the Catalan, Motzkin and Schröder numbers