Handbook of theoretical computer science (vol. B)
Journal of Algorithms
The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations (Art of Computer Programming)
ACM Computing Surveys (CSUR)
The origins of combinatorics on words
European Journal of Combinatorics
Indexing permutations for binary strings
Information Processing Letters
On table arrangements, scrabble freaks, and jumbled pattern matching
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Sub-quadratic time and linear space data structures for permutation matching in binary strings
Journal of Discrete Algorithms
Binary jumbled string matching for highly run-length compressible texts
Information Processing Letters
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We present a new class of binary words: the prefix normal words. They are defined by the property that for any given length k, no factor of length k has more a's than the prefix of the same length. These words arise in the context of indexing for jumbled pattern matching (a.k.a. permutation matching or Parikh vector matching), where the aim is to decide whether a string has a factor with a given multiplicity of characters, i.e., with a given Parikh vector. Using prefix normal words, we give the first non-trivial characterization of binary words having the same set of Parikh vectors of factors. We prove that the language of prefix normal words is not context-free and is strictly contained in the language of pre-necklaces, which are prefixes of powers of Lyndon words. We discuss further properties and state open problems.