Herbert J. Ryser is widely regarded as one of the major figures in combinatorics in the 20th century. His Combinatorial Mathematics is a classic which has enticed many young mathematics students into this area.
This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves.
Herbert J. Ryser is widely regarded as one of the major figures in combinatorics in the 20th century. His Combinatorial Mathematics is a classic which has enticed many young mathematics students into this area.
Combinatorial Algorithms for Computers and Calculators, Second Edition deals with combinatorial algorithms for computers and calculators. Topics covered range from combinatorial families such as the random subset and k-subset of an n-set and Young tableaux, to combinatorial structures including the cycle structure of a permutation and the spanning forest of a graph. Newton forms of a polynomial and the composition of power series are also discussed. Comprised of 30 chapters, this volume begins with an introduction to combinatorial algorithms by considering the generation of all of the 2n subsets of the set {1, 2,...,n}. The discussion then turns to the random subset and k-subset of an n-set; next composition of n into k parts; and random composition of n into k parts. Subsequent chapters focus on sequencing, ranking, and selection algorithms in general combinatorial families; renumbering rows and columns of an array; the cycle structure of a permutation; and the permanent function. Sorting and network flows are also examined, along with the backtrack method and triangular numbering in partially ordered sets. This book will be of value to both students and specialists in the fields of applied mathematics and computer science.
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