Pascal pyramids and their applications. (Q2723295)

This book is devoted to arithmetical, geometrical and combinatorial properties of arithmetical triangles and pyramids that generalize the Pascal triangle and their applications to partition polynomials, difference and differential operators, planar rooted trees and models of random processes. NEWLINENEWLINENEWLINEThe chapters of the book are the following: Pascal triangle and its generalizations (Pascal triangle and its binomial coefficients, other arithmetical triangles, generalized Pascal triangle, \(A\)- and \(B\)-triangles and their properties), Pascal pyramid and its generalizations (Pascal pyramid and its trinomial coefficients, generalized Pascal pyramid), \(A\)- and \(B\)-pyramids and their properties (generalized trinomial coefficients, generalized Tribonacci numbers and their recurrence relations and generating functions), Combinatorial partition polynomials (homogeneous Bell and Platonov polynomials, Touchard polynomials, generalized \(A\)- and \(B\)-polynomials), Operators and algorithms (difference and differential operators, mutual transformation algorithms), Finite graphs and paths (Motzkin and MacMahon paths, planar rooted trees), Models of random processes (random walks, discrete renewal processes, homogeneous branching processes). The bibliography contains 355 titles. NEWLINENEWLINENEWLINEThe book is mainly intended to all people interested in discrete mathematics and university and college students.