Determinants of Triangular Matrices and Trajectories on Ferre Diagrams

Some functions defined on the set of integer triangular matrices and their modifications are considered. These functions are analogs of the classical determinant and permanent functions and provide a powerful apparatus for studying sequences generated by linear recursive equations. Modifications of these functions are used to solve the problem about trajectories on Ferre diagrams and to establish new combinatorial identities.     

Generalization of the ballot numbers

Mathematical Notes - The paper is devoted to a generalization of the ballot numbers related to a random walk.     

Triangular matrices and combinatorial inversion formulas

The paper is devoted to the construction of the matrix inverse of an infinite triangular matrix and to finding the connection coefficients between polynomial sequences and general combinatorial inversion formulas.     

A relationship between determinants and permanents

Mathematical Notes - A class of matrices is determined for which a Polya transformation of permanents into determinants can be defined.