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- W2024991606 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." @default.
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- W2024991606 date "2015-08-01" @default.
- W2024991606 modified "2023-10-15" @default.
- W2024991606 title "Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method" @default.
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- W2024991606 doi "https://doi.org/10.1016/j.ejc.2015.02.022" @default.
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