Solving the recognition problem of Lorenz braids via matrices of inversions for permutations

E. A. Elrifai; Redha. A. Alghamdi

E. A. Elrifai Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdul Rahman University, Kingdom of Saudi Arabia
Redha. A. Alghamdi Deanship of Scientific Research, Princess Nourah Bint Abdul Rahman University, Kingdom of Saudi Arabia

Keywords: Lorenz Knots and links, Braid groups, Matrices of inversions for permutations.

Abstract

In this work, we present some needed results about matrices of inversions for permutations. Then we apply it for solving the recognition problem of Lorenz braids. Each Lorenz braid is uniquely determined by a unique simple binary matrix. Then, we got a quick algorithm for counting the trip number (minimal braid index) hence, crossing number and minimal braid representative of the Lorenz knots.

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