Constructive Combinatorics

ISBN-13: 9780387963471 / Angielski / Twarda / 1986 / 186 str.

Royal Stanton; D. W. Stanton; D. E. White

Opis

The notes that eventually became this book were written between 1977 and 1985 for the course called Constructive Combinatorics at the University of Minnesota. This is a one-quarter (10 week) course for upper level undergraduate students. The class usually consists of mathematics and computer science majors, with an occasional engineering student.

Spis treści

1 Listing Basic Combinatorial Objects.- 1.1 Permutations.- 1.2 Subsets.- 1.3 Integer Partitions.- 1.4 Product Spaces.- 1.5 Set Partitions.- Notes.- Exercises.- 2 Partially Ordered Sets.- 2.1 Six Posets.- 2.2 Matching the Boolean Algebra.- 2.3 The Littlewood-Offord Problem.- 2.4 Extremal Set Theory.- Notes.- Exercises.- 3 Bijections.- 3.1 The Catalan Family.- 3.2 The Prüfer Correspondence.- 3.3 Partitions.- 3.4 Permutations.- 3.5 Tableaux.- 3.6 The Schensted Correspondence.- 3.7 Properties of the Schensted Correspondence.- Notes.- Exercises.- 4 Involutions.- 4.1 The Euler Pentagonal Number Theorem.- 4.2 Vandermonde’s Determinant.- 4.3 The Cayley-Hamilton Theorem.- 4.4 The Matrix-Tree Theorem.- 4.5 Lattice Paths.- 4.6 The Involution Principle.- Notes.- Exercises.- A.1 Permutations.- A.2 Subsets.- A.3 Set Partitions.- A.4 Integer Partitions.- A.5 Product Spaces.- A.6 Match to First Available.- A.7 The Schensted Correspondence.- A.8 The Prüfer Correspondence.- A.9 The Involution Principle.