Transposition invariant words

Transposition invariant words

We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transposition invariant words have a simple interpretation by means of elementary group theory. This leads us to investigate some p...

Transposition invariant string matching

Given strings A = a1a2 . . . am and B = b1b2 . . . bn over an alphabet Σ ⊆ U, where U is some numerical universe closed under addition and subtraction, and a distance function d(A,B) that gives the score of the best (partial) matching of A and B, the transposition invariant distance is mint∈U{d(A+ t,B)}, where A+ t = (a1 + t)(a2 + t) . . . (am + t). We study the problem of computing the transpo...

Transposition Invariant String Mat hing ⋆

Veli Mäkinen a,1, Gonzalo Navarro b,2, and Esko Ukkonen a,1 aDepartment of Computer S ien e, P.O Box 26 (Teollisuuskatu 23), FIN-00014 University of Helsinki, Finland. bCenter for Web Resear h, Department of Computer S ien e, University of Chile Blan o En alada 2120, Santiago, Chile. Abstra t Given strings A = a1a2 . . . am and B = b1b2 . . . bn over an alphabet Σ ⊆ U, where U is some numeri al...

Algorithms for Transposition Invariant String

Transposition-Invariant Self-Similarity Matrices

Self-similarity matrices have become an important tool for visualizing the repetitive structure of a music recording. Transforming an audio data stream into a feature sequence, one obtains a self-similarity matrix by pairwise comparing all features of the sequence with respect to a local cost measure. The basic idea is that similar audio segments are revealed as paths of low cost along diagonal...