Combinatorics and Matrix Theory have a symbiotic, or mutually
beneficial, relationship. This relationship is discussed in my paper The
symbiotic relationship of combinatorics and matrix theoryl where I
attempted to justify this description. One could say that a more
detailed justification was given in my book with H. J. Ryser entitled
Combinatorial Matrix Theon? where an attempt was made to give a broad
picture of the use of combinatorial ideas in matrix theory and the use
of matrix theory in proving theorems which, at least on the surface, are
combinatorial in nature. In the book by Liu and Lai, this picture is
enlarged and expanded to include recent developments and contributions
of Chinese mathematicians, many of which have not been readily available
to those of us who are unfamiliar with Chinese journals. Necessarily,
there is some overlap with the book Combinatorial Matrix Theory. Some of
the additional topics include: spectra of graphs, eulerian graph
problems, Shannon capacity, generalized inverses of Boolean matrices,
matrix rearrangements, and matrix completions. A topic to which many
Chinese mathematicians have made substantial contributions is the
combinatorial analysis of powers of nonnegative matrices, and a large
chapter is devoted to this topic. This book should be a valuable
resource for mathematicians working in the area of combinatorial matrix
theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear
Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press,
1991.
