This book can be read at several levels. Those whose only need is to use one of the computer programs can turn immediately to those pages and satisfy their wants. Thus, on one level, this is a collection of subroutines, in FORTRAN, for the solution of combinatorial problems. At the other extreme, pure mathematicians with no need of computer programs will find much that is new and hopefully interesting in these pages.

Readers will want to follow the entire road from general mathematics to particular mathematics to informal algorithm to formal algorithm to computer program and back again, which occurs in virtually every chapter of the book.
Readers will view methods and programs as a beginning set of building blocks for their own kit of tools and will go on to add to these tools to meet their own needs, so that the contents of this book will be not a collection of pretty artifacts to be looked at but basic elements of the growing and working equipment of scientific investigation and learning.

Contents
Preface to Second Edition
Preface to First Edition
Introduction
Aims
Highlights
Categories of Usage (Part I)
Structure of the Chapters
The Specifications List
Structure of the "Next" Programs
Structure of the "Random" Programs
Arrays and Specifications
PART 1 COMBINATORIAL FAMILIES
1 Next Subset of an n-Set (NEXSUBILEXSUB)
(A) The Direct Approach
(B) The Gray Code
Algodthm NEXSUB
(C) Lexicographic Sequencing
Algorithm LEXSUB
Subroutine Specifications (NEXSUB)
Subroutine Specifications (LEXSUB)
Sample Output (NEXSUB)
2 Random Subset of an n-Set (RANSUB)
Algorithm RANSUB
Subroutine Specifications
Sample Output
3 Next k-Subset of an n-Set (NEXKSB/NXKSRD)
Algorithm NEXKSB (Lexicographic)
Flow Chart NXKSRD
Subroutine Specifications (NEXKSB)
Subroutine Specifications (NXKSRD)
Sample Output (NEXKSBj
Sample Output (NXKSRDj
4 Random k-Subset of an n-Set (RANKSB)
Algorithm RANKSB
Algorithm RKS2
Subroutine Specifications
Sample Intermediate Result
Sample Output
5 Next Composition of n into k Parts (NEXCOM)
Algorithm NEXCOM
Subroutine Specifications
Sample Output
6 Random Composition of n into k Parts (RANCOM)
Algorithm RANCOM
Subroutine Specifications
7 Next Permutation of n Letters (NEXPER)
Algorithm NEXPER
Subroutine Specifications
Sample Output
8 Random Permutation of n Letters (RANPER)
Algorithm RANPER
Subroutine Specifications
Sample Output
9 Next Partition of Integer n (NEXPAR)
Algorithm NEXPAR
Subroutine Specifications
10 Random Partition of an Integer n (RANPAR)
Algorithm RANPAR
Subroutine Specifications
Sample Output
Postscript: Deus ex Machina
Algorithm NEXT PLANE PARTITION
11 Next Partition of an n-Set (NEXEQU)
Algorithm NEXEQU
Subroutine Specifications
Sample Output
12 Random Partition of an n-Set (RANEQU)
Algorithm RANEQU
Flow Chart RANEQU
Subroutine Specifications
Sample Output
13 Sequencing, Ranking, and Selection Algorithms in General Combinatorial Families (SELECT)
(A) Introduction
(B) General Setting
Algorithm NEXT
(C) Examples
(D) The Formal Algorithms
Algorithm SELECT
Subroutine Specifications
(E) Decoding
Sample Output
14 Young Tableaux (NEXYTBIRANYTB)
(A) Introduction
(B) Lexicographic Sequencing
Algorithm NEXYTB
(e) Random Selection
Algorithm RANYTB
Subroutine Specifications (NEXYTB)
Subroutine Speciflcation.s (RANYTB)
Sample Output
PART 2 COMBINATORIAL STRUCTURES
15 Sorting (HPSORT/EXHEAP)
Algorithm [!F(l, 11)
Algorithm TOHEAP
Algorithm SORTHEAP
Subroutine Specifications (HPSORT)
Subroutine Specifications (EXHEAP)
Sample Output
16 The Cycle Structure of a Pennutation (CYCLES)
Algorithm TAG
Algorithm INVERT
Subroutine Specifications
Sample Output
17 Renumbering Rows and Columns ofan Array (RENUMB)
Algorithm RENUMB
Subroutine Specifications
Sample Output
18 Spanning Forest of a Graph (SPANFO)
(A) Introduction
(B) Depth-First-Search
Algorithm DEPTHFIRST
(C) A Breadth-First Algorithm
Algorithm LINK (x, e, n, E)
Algorithm VISIT (x, E. n, E, q, Ii> mil a)
Algorithm SCAN (x, E, n, E, p,Io, mo, m, r)
Algorithm COMPONENT (x, e, n, E, p, k, L)
Algorithm SPANFO (x, e, n, E, k)
Subroutine Specifications
Sample Output
19 Newton Fonns of a Polynomial (POLY)
Algorithm VALUE
Algorithm NEWTON
Algorithm TAYLOR
Algorithm STIRLING
Algorithm REVERSE STIRLING
Algorithm NWT (m, x, E, Y)
Subroutine Specincations
Sample Output
20 Chromatic Polynomial of a Graph (CHROMP)
Algorithm CHROMP
Subroutine Specifications
Sample Output
21 Composition of Power Series (POWSER)
Algorithm POWSER (Options I, 2, and 3)
Algorithm POWSER (Option 4)
Subroutine Specifications
First Sample Output, Option 1
Second Sample Output, Option 1
Sample Output, Option 3
Sample Output, Option 4
22 Network Flows (NETFLO)
Algorithm SWAP (i,j Option)
Algorithm INIT
Algorithm SORT
Algorithm XREF
Algorithm KZNET
Algorithm PUSHOUT (p, P)
Algorithm OLDFLOW (p)
Algorithm PUSHBACK (p)
Flow Chart PREFLOW
Algorithm PREFLOW
Algorithm NETFLO (n, E, E, y, source, sink, a, b, c, d, x)
Subroutine Specifications
Sample Output
23 The Pennanent Function (PERMAN)
Computation of the Pemmnent Function
Algorithm PERMAN
Subroutine Specifications
Sample Output
24 Invert a Triangular Array (INVERT)
Algorithm INVERT
Subroutine Specifications
25 Triangular Numbering in Partially Ordered Sets (TRIANG)
Algorithm TRIANG
Subroutine Speci.6.cations
Sample Output
26 The Mobius Function (MOBIUS)
Subroutine Specifications
Sample Output
27 The Backtrack Method (BACKTR)
(A) General (BACKTR)
Flow Chart BACKTR
Subroutine Specifications
(B) Coloring the Vertices of a Graph (COLVRT)
Subroutine Specifications
Sample Output
(C) Euler Circuit, (EULCRC)
Algorithm EULCRC
Subroutine Specifications
Sample Output
(D) Hamilton Circuits (HAMCRC)
Subroutine Specifications
Sample Output 1
Sample Output 2
(E) Spanning T'ees (SPNTRE)
Subroutine Specifications
Sample Output
28 Labeled Trees (LBLTRE)
Algmithm LBLTRE
Subroutine Specifications
Sample Output
29 Random Unlabeled Rooted Trees (RANRUT)
Algo,ithm RANRUT
Subroutine Specifications
Sample Output
30 Tree of Minimal Length (MINSPT)
Algorithm MINSPT
Subroutine Specifications
Sample Output
Exercises
Bibliographic Notes
References
Index