Subword histories and Parikh matrices

Mateescu, Alexandru; Salomaa, Arto; Yü, Sheng

doi:10.1016/j.jcss.2003.04.001

Cited by 66 publications

(57 citation statements)

References 8 publications

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“…In recent decades many techniques have been developed to solve complex problems of words using Parikh Matrix. It is cited a few examples [8,[10][11][12][14][15][16][17][19][20] which have used subword occurrences and Parikh matrix for solving the problems of word. The problem of M-ambiguity is dealt in the following papers [1][2][3]18].…”

Section: Introductionmentioning

confidence: 99%

On M-ambiguity of Words corresponding to a Parikh Matrix

Bhattacharjee¹

2017

IJCA

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Section: Introductionmentioning

confidence: 99%

On M-ambiguity of Words corresponding to a Parikh Matrix

Bhattacharjee¹

2017

IJCA

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“…The Parikh matrix of a word gives more numerical information about a word than a Parikh vector does. There has been a series of studies [1,2,3,8,13,14,19,20,21,22,23,24,25,26,27] on the properties of Parikh matrix. One such property is the injectivity of the Parikh matrix mapping.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Subramanian

Mahalingam

Abdullah

et al. 2013

Int. J. Found. Comput. Sci.

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Abstract:Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays $A$ and $B$ are defined to be $M-$equivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of $M-$ambiguity to a picture array. In the binary and ternary cases, conditions that ensure $M-$ambiguity are then obtained. Response to Reviewers:The authors are again grateful to the referee for a very meticulous reading of the revised version1 and thank the referee for further suggestions on improving the work. The authors have now revised the paper and revision2 has been submitted.Details of the changes done in revision2 are listed in "Author Response to comments on revision 1" as responses to the comments. Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays A and B are defined to be M −equivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of M −ambiguity to a picture array. In the binary and ternary cases, conditions that ensure M −ambiguity are then obtained. Powered by Editorial Manager® and Preprint Manager® from Aries Systems Corporation

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“…, i t ) of increasing positive integers, where for 1 j t, the jth letter of u is the i j th letter of w. (The indexing of words begins at position 1.) For instance, the six occurrences of u = aba in w = abaabab are (1,2,3), (1,2,4), (1,2,6), (1,5,6), (3,5,6), (4,5,6).…”

Section: Introductionmentioning

confidence: 99%

Subword balance, position indices and power sums

Salomaa

2010

Journal of Computer and System Sciences

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In this paper, we investigate various ways of characterizing words, mainly over a binary alphabet, using information about the positions of occurrences of letters in words. We introduce two new measures associated with words, the position index and sum of position indices. We establish some characterizations, connections with Parikh matrices, and connections with power sums. One particular emphasis concerns the effect of morphisms and iterated morphisms on words.

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Subword histories and Parikh matrices

Cited by 66 publications

References 8 publications

On M-ambiguity of Words corresponding to a Parikh Matrix

On M-ambiguity of Words corresponding to a Parikh Matrix

Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Subword balance, position indices and power sums

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