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Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method

 

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Opened Access Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method
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Author: Falcón Ganfornina, Raúl Manuel
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I
Date: 2015
Published in: European Journal of Combinatorics, 48, 215-223.
Document type: Article
Abstract: The current paper deals with the enumeration and classification of the set SORr,n of self-orthogonal r × r partial Latin rectangles based on n symbols. These combinatorial objects are identified with the independent sets of a Hamming graph and with the zeros of a radical zero-dimensional ideal of polynomials, whose reduced Gröbner basis and Hilbert series can be computed to determine explicitly the set SORr,n. In particular, the cardinality of this set is shown for r ≤ 4 and n ≤ 9 and several formulas on the cardinality of SORr,n are exposed, for r ≤ 3. The distribution of r × s partial Latin rectangles based on n symbols according to their size is also obtained, for all r, s, n ≤ 4.
Cite: Falcón Ganfornina, R.M. (2015). Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method. European Journal of Combinatorics, 48, 215-223.
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URI: http://hdl.handle.net/11441/67848

DOI: 10.1016/j.ejc.2015.02.022

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