, Contents
Preface page ix
1 The Very Basics of Stringology 1
2 Combinatorial Puzzles 17
1 Stringologic Proof of Fermat’s Little Theorem 18
2 Simple Case of Codicity Testing 19
3 Magic Squares and the Thue–Morse Word 20
4 Oldenburger–Kolakoski Sequence 22
5 Square-Free Game 24
6 Fibonacci Words and Fibonacci Numeration System 26
7 Wythoff’s Game and Fibonacci Word 28
8 Distinct Periodic Words 30
9 A Relative of the Thue–Morse Word 33
10 Thue–Morse Words and Sums of Powers 34
11 Conjugates and Rotations of Words 35
12 Conjugate Palindromes 37
13 Many Words with Many Palindromes 39
14 Short Superword of Permutations 41
15 Short Supersequence of Permutations 43
16 Skolem Words 45
17 Langford Words 48
18 From Lyndon Words to de Bruijn Words 50
3 Pattern Matching 53
19 Border Table 54
20 Shortest Covers 56
21 Short Borders 58
v
,vi Contents
22 Prefix Table 60
23 Border Table to the Maximal Suffix 62
24 Periodicity Test 65
25 Strict Borders 67
26 Delay of Sequential String Matching 70
27 Sparse Matching Automaton 72
28 Comparison-Effective String Matching 74
29 Strict Border Table of the Fibonacci Word 76
30 Words with Singleton Variables 78
31 Order-Preserving Patterns 81
32 Parameterised Matching 83
33 Good-Suffix Table 85
34 Worst Case of the Boyer–Moore Algorithm 88
35 Turbo-BM Algorithm 90
36 String Matching with Don’t Cares 92
37 Cyclic Equivalence 93
38 Simple Maximal Suffix Computation 96
39 Self-Maximal Words 98
40 Maximal Suffix and Its Period 100
41 Critical Position of a Word 103
42 Periods of Lyndon Word Prefixes 105
43 Searching Zimin Words 107
44 Searching Irregular 2D Patterns 110
4 Efficient Data Structures 111
45 List Algorithm for Shortest Cover 112
46 Computing Longest Common Prefixes 113
47 Suffix Array to Suffix Tree 115
48 Linear Suffix Trie 119
49 Ternary Search Trie 122
50 Longest Common Factor of Two Words 124
51 Subsequence Automaton 126
52 Codicity Test 128
53 LPF Table 130
54 Sorting Suffixes of Thue–Morse Words 134
55 Bare Suffix Tree 137
56 Comparing Suffixes of a Fibonacci Word 139
57 Avoidability of Binary Words 141
58 Avoiding a Set of Words 144
, vii
59 Minimal Unique Factors 146
60 Minimal Absent Words 148
61 Greedy Superstring 152
62 Shortest Common Superstring of Short Words 155
63 Counting Factors by Length 157
64 Counting Factors Covering a Position 160
65 Longest Common-Parity Factors 161
66 Word Square-Freeness with DBF 162
67 Generic Words of Factor Equations 164
68 Searching an Infinite Word 166
69 Perfect Words 169
70 Dense Binary Words 173
71 Factor Oracle 175
5 Regularities in Words 180
72 Three Square Prefixes 181
73 Tight Bounds on Occurrences of Powers 183
74 Computing Runs on General Alphabets 185
75 Testing Overlaps in a Binary Word 188
76 Overlap-Free Game 190
77 Anchored Squares 192
78 Almost Square-Free Words 195
79 Binary Words with Few Squares 197
80 Building Long Square-Free Words 199
81 Testing Morphism Square-Freeness 201
82 Number of Square Factors in Labelled Trees 203
83 Counting Squares in Combs in Linear Time 206
84 Cubic Runs 208
85 Short Square and Local Period 210
86 The Number of Runs 212
87 Computing Runs on Sorted Alphabet 214
88 Periodicity and Factor Complexity 219
89 Periodicity of Morphic Words 220
90 Simple Anti-powers 222
91 Palindromic Concatenation of Palindromes 224
92 Palindrome Trees 225
93 Unavoidable Patterns 227
Preface page ix
1 The Very Basics of Stringology 1
2 Combinatorial Puzzles 17
1 Stringologic Proof of Fermat’s Little Theorem 18
2 Simple Case of Codicity Testing 19
3 Magic Squares and the Thue–Morse Word 20
4 Oldenburger–Kolakoski Sequence 22
5 Square-Free Game 24
6 Fibonacci Words and Fibonacci Numeration System 26
7 Wythoff’s Game and Fibonacci Word 28
8 Distinct Periodic Words 30
9 A Relative of the Thue–Morse Word 33
10 Thue–Morse Words and Sums of Powers 34
11 Conjugates and Rotations of Words 35
12 Conjugate Palindromes 37
13 Many Words with Many Palindromes 39
14 Short Superword of Permutations 41
15 Short Supersequence of Permutations 43
16 Skolem Words 45
17 Langford Words 48
18 From Lyndon Words to de Bruijn Words 50
3 Pattern Matching 53
19 Border Table 54
20 Shortest Covers 56
21 Short Borders 58
v
,vi Contents
22 Prefix Table 60
23 Border Table to the Maximal Suffix 62
24 Periodicity Test 65
25 Strict Borders 67
26 Delay of Sequential String Matching 70
27 Sparse Matching Automaton 72
28 Comparison-Effective String Matching 74
29 Strict Border Table of the Fibonacci Word 76
30 Words with Singleton Variables 78
31 Order-Preserving Patterns 81
32 Parameterised Matching 83
33 Good-Suffix Table 85
34 Worst Case of the Boyer–Moore Algorithm 88
35 Turbo-BM Algorithm 90
36 String Matching with Don’t Cares 92
37 Cyclic Equivalence 93
38 Simple Maximal Suffix Computation 96
39 Self-Maximal Words 98
40 Maximal Suffix and Its Period 100
41 Critical Position of a Word 103
42 Periods of Lyndon Word Prefixes 105
43 Searching Zimin Words 107
44 Searching Irregular 2D Patterns 110
4 Efficient Data Structures 111
45 List Algorithm for Shortest Cover 112
46 Computing Longest Common Prefixes 113
47 Suffix Array to Suffix Tree 115
48 Linear Suffix Trie 119
49 Ternary Search Trie 122
50 Longest Common Factor of Two Words 124
51 Subsequence Automaton 126
52 Codicity Test 128
53 LPF Table 130
54 Sorting Suffixes of Thue–Morse Words 134
55 Bare Suffix Tree 137
56 Comparing Suffixes of a Fibonacci Word 139
57 Avoidability of Binary Words 141
58 Avoiding a Set of Words 144
, vii
59 Minimal Unique Factors 146
60 Minimal Absent Words 148
61 Greedy Superstring 152
62 Shortest Common Superstring of Short Words 155
63 Counting Factors by Length 157
64 Counting Factors Covering a Position 160
65 Longest Common-Parity Factors 161
66 Word Square-Freeness with DBF 162
67 Generic Words of Factor Equations 164
68 Searching an Infinite Word 166
69 Perfect Words 169
70 Dense Binary Words 173
71 Factor Oracle 175
5 Regularities in Words 180
72 Three Square Prefixes 181
73 Tight Bounds on Occurrences of Powers 183
74 Computing Runs on General Alphabets 185
75 Testing Overlaps in a Binary Word 188
76 Overlap-Free Game 190
77 Anchored Squares 192
78 Almost Square-Free Words 195
79 Binary Words with Few Squares 197
80 Building Long Square-Free Words 199
81 Testing Morphism Square-Freeness 201
82 Number of Square Factors in Labelled Trees 203
83 Counting Squares in Combs in Linear Time 206
84 Cubic Runs 208
85 Short Square and Local Period 210
86 The Number of Runs 212
87 Computing Runs on Sorted Alphabet 214
88 Periodicity and Factor Complexity 219
89 Periodicity of Morphic Words 220
90 Simple Anti-powers 222
91 Palindromic Concatenation of Palindromes 224
92 Palindrome Trees 225
93 Unavoidable Patterns 227
