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Combinatorics of Periods in Strings
"... We consider the set (n) of all period sets of strings of length n over a nite alphabet. We show that there is redundancy in period sets and introduce the notion of an irreducible period set. We prove that (n) is a lattice under set inclusion and does not satisfy the JordanDedekind condition. We ..."
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We consider the set (n) of all period sets of strings of length n over a nite alphabet. We show that there is redundancy in period sets and introduce the notion of an irreducible period set. We prove that (n) is a lattice under set inclusion and does not satisfy the JordanDedekind condition. We propose the rst enumeration algorithm for (n) and improve upon the previously known asymptotic lower bounds on the cardinality of (n). Finally, we provide a new recurrence to compute the number of strings sharing a given period set. 1
Automata and Formal Languages
, 2003
"... This article provides an introduction to the theory of automata and formal languages. The elements are presented in a historical perspective and the links with other areas are underlined. In particular, applications of the field to linguistics, software design, text processing, computational alg ..."
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This article provides an introduction to the theory of automata and formal languages. The elements are presented in a historical perspective and the links with other areas are underlined. In particular, applications of the field to linguistics, software design, text processing, computational algebra or computational biology are given.
Electronic Colloquium on Computational Complexity, Report No. 59 (2004) Randomized Quicksort and the Entropy of the Random Number Generator
, 2004
"... The worstcase complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds an ..."
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The worstcase complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from n log n to n 2, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded minentropy, the geometrical distribution and the δrandom source. 1
A census of edgetransitive planar tilings
, 2009
"... Recently Graves, Pisanski and Watkins have determined the growth rates of Bilinski diagrams of oneended, 3connected, edgetransitive planar maps. The computation depends solely on the edgesymbol 〈p, q; k, l 〉 that was introduced by B. Grünbaum and G. C. Shephard in their classification of such p ..."
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Recently Graves, Pisanski and Watkins have determined the growth rates of Bilinski diagrams of oneended, 3connected, edgetransitive planar maps. The computation depends solely on the edgesymbol 〈p, q; k, l 〉 that was introduced by B. Grünbaum and G. C. Shephard in their classification of such planar tessellations. We present a census of such tessellations in which we describe some of their properties, such as whether the edgetransitive planar tessellation is vertex or facetransitive, selfdual, bipartite or Eulerian. In particular, we order such tessellations according to the growth rate and count the number of tessellations in each subclass. 1 1