Generalized Schröder matrix and its combinatorial interpretation

DOI10.1080/03081087.2017.1301360zbMath1387.15004OpenAlexW2595273038MaRDI QIDQ4640078

Victor F. Sirvent, José L. Ramírez

Publication date: 16 May 2018

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2017.1301360

zbMATH Keywords

lattice pathRiordan arrayDelannoy matrixSchröder matrix

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Theory of matrix inversion and generalized inverses (15A09) Permutations, words, matrices (05A05) Special matrices (15B99)

Related Items (10)

Unnamed Item ⋮ Equivalence of the descents statistic on some (4,4)-avoidance classes of permutations ⋮ Unnamed Item ⋮ The \(\mathfrak{uvu}\)-avoiding \((a, b, c)\)-generalized Motzkin paths with vertical steps: bijections and statistic enumerations ⋮ The halves of Delannoy matrix and Chung-Feller properties of the \(m\)-Schröder paths ⋮ Generalized Schröder matrices arising from enumeration of lattice paths ⋮ On Ward's differential calculus, Riordan matrices and Sheffer polynomials ⋮ Unimodality, linear recurrences and combinatorial properties associated to rays in the generalized Delannoy matrix ⋮ Enumerating several aspects of non-decreasing Dyck paths ⋮ Endomorphisms of the Riordan group

Uses Software

• OEIS

Cites Work

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• A generalization of the \(k\)-bonacci sequence from Riordan arrays
• Schröder matrix as inverse of Delannoy matrix
• Weighted lattice paths
• Why Delannoy numbers?
• On Some Alternative Characterizations of Riordan Arrays
• Pascal's Matrices
• A bijective proof of the equation linking the Schröder numbers, large and small
• The linear algebra of the generalized Pascal matrix

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