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

Raúl M. Falcón
2013 The Seventh European Conference on Combinatorics, Graph Theory and Applications  
The current paper deals with the enumeration and classification of the set SOR r,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 SOR r,n . In particular, the cardinality of this set is shown for r ≤ 4 and n ≤ 9 and
more » ... formulas on the cardinality of SOR r,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.
doi:10.1007/978-88-7642-475-5_96 fatcat:72rf7cbgfrauhmm6wip6jg6h7q