Please use this identifier to cite or link to this item:
Title: Determinants of some Hessenberg–Toeplitz matrices with Motzkin number entries
Authors: Гой, Тарас Петрович
Shattuck, Mark
Keywords: Motzkin number
Motzkin path
Riordan number
Catalan number
Hessenberg-Toeplitz matrix
Trudi’s formula
generating function
Issue Date: 2023
Citation: Goy T., Shattuck M. Determinants of some Hessenberg–Toeplitz matrices with Motzkin number entries. Journal of Integer Sequences. 2023. Vol. 26. Article 23.3.4
Abstract: In this paper, we find formulas for the determinants of some Hessenberg–Toeplitz matrices whose nonzero entries are derived from the Motzkin number sequence and its translates. We provide both algebraic and combinatorial proofs of our results, making use of generating functions for the former and various counting methods, such as direct enumeration, sign-changing involutions, and bijections, for the latter. In the process, it is shown that three important classes of lattice paths—namely, the Motzkin paths, the Riordan paths, and the so-called Motzkin left factors—have their cardinalities given as determinants of certain Hessenberg–Toeplitz matrices with Motzkin number entries. Further formulas are found for determinant identities involving two sequences from the On-Line Encyclopedia of Integer Sequences, which are subsequently explained bijectively.
Appears in Collections:Статті та тези (ФМІ)

Files in This Item:
File Description SizeFormat 
sh36.pdf248.72 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.