Combinatorial Enumeration Book

	Notation	xxiii
1	Mathematical Preliminaries	1
1.1	The Ring of Formal Power Series	1
1.2	The Lagrange Theorem for Implicit Functions	15
2	The Combinatorics of the Ordinary Generating Function	29
2.1	Introduction	29
2.2	The Elementary Counting Lemmas	31
2.3	Preliminary Examples	48
2.4	Sequences	62
2.5	Partitions of an Integer	80
2.6	Inversions in Permutations and q-Identities	96
2.7	Planted Plane Trees	109
2.8	Sequences with Distinguished Substrings	128
2.9	Rooted Planar Maps and the Quadratic Method	138
3	The Combinatorics of the Exponential Generating Function	158
3.1	Introduction	158
3.2	The Elementary Counting Lemmas	160
3.3	Trees and Cycles in Permutations and Functions	170
3.4	2-Covers of a Set and Homeomorphically Irreducible Labeled Graphs	197
3.5	Coefficient Extraction for Symmetric Functions	213
4	The Combinatorics of Sequences	230
4.1	Introduction	230
4.2	The Maximal String Decomposition Theorem	231
4.3	The Pattern Algebra	243
4.4	The Logarithmic Connection for Circular Permutations	268
4.5	Permanents and Absolute Problems	281
5	The Combinatorics of Paths	290
5.1	Introduction	290
5.2	Weighted Paths	291
5.3	Lattice Paths	313
5.4	Ordered Sets of Paths	322
5.5	A q-Analogue of the Lagrange Theorem	330
	Solutions	339
	Chapter 1	339
	Chapter 2	350
	Chapter 3	414
	Chapter 4	457
	Chapter 5	513
	References	542
	Index	553