Determinants of triangular matrices and trajectories on Ferre diagrams
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.
scientific article; zbMATH DE number 1928344