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%I #19 Oct 17 2019 21:05:52
%S 0,1,14,1446,705366,1304451482
%N Number of n X n checkered tori (see A179043) with at least one 0 and at least one 1 in each row and each column.
%C Let us denote by Qn the set of all n X n binary matrices with at least one 0 and at least one 1 in each row and each column. Let A,B belong to Qn. We will say that A and B are equivalent if B is obtained from A as a result of a sequential cyclic move of the last row or column at a first position. [Please rewrite that sentence!] It's easy to see that this defines an equivalence relation. The sequence gives the number of equivalence classes. The elements of the factor-set Qn/~ are relevant in the textile industry.
%H K. Yordzhev, <a href="http://www.math.bas.bg/smb/2009_PK/tom_2009/pdf/196-202.pdf">An example for the use of bitwise operations in programming</a>, Mathematics and education in mathematics, v. 38 (2009), 196-202, also arXiv:1201.1468 [cs.OH], 2012.
%H K. Yordzhev, H. Kostadinova, <a href="http://dx.doi.org/10.18052/www.scipress.com/BMSA.1.16">Mathematical Modelling in the Textile Industry</a> Bulletin of Mathematical Sciences & Applications, Vol. 1, No. 1 (2012), pp. 20 -35.
%Y Cf. A179043.
%K nonn,more
%O 1,3
%A _Krasimir Yordzhev_, Mar 24 2016
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