Determinants of triangular matrices and trajectories on Ferre diagrams
type: Item
instance of: scholarly article
title: Determinants of triangular matrices and trajectories on Ferre diagrams
zbMATH Open document ID: 1025.15010
DOI: 10.1023/A:1021433728200
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Definitions of paradeterminants, parapermanents and their modifications, i.e., upper and lower \(F\)-paradeterminants and upper and lower \(F\)-parapermanents of integer triangular matrices are given and their properties are discussed. The parapermanents are applied to solve recursive equations of the \(k\)th order with constant coefficients without necessity to solve the corresponding algebraic equation. Examples showing the application of upper \(F\)-determinants at finding the number of shortest paths on Ferre and skew diagrams are given. The Ferre diagrams can be used to obtain new interesting recursions for upper \(F\)-paradeterminants.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B36
zbMATH DE Number: 1928344
zbMATH Keywords: paradeterminant
zbMATH Keywords: parapermanent
zbMATH Keywords: \(F\)-paradeterminant
zbMATH Keywords: \(F\)-parapermanent
zbMATH Keywords: skew diagram
zbMATH Keywords: Ferre diagram
zbMATH Keywords: shortest path
zbMATH Keywords: partition of positive integer
zbMATH Keywords: integer triangular matrices
author: R. A. Zators'kyj
MaRDI profile type: Publication
full work available at URL: a:1021433728200
OpenAlex ID: W199235764
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description: scientific article; zbMATH DE number 1928344