On an Algorithm for Obtaining All Binary Matrices of Special Class Releted to V. E. Tarakanov’s Formula

Krasimir Yordzhev^1,

¹Faculty of Mathematics and Natural Sciences, South-West University “N. Rilsky”, Blagoevgrad, Bulgaria

Cite this paper:
Krasimir Yordzhev. On an Algorithm for Obtaining All Binary Matrices of Special Class Releted to V. E. Tarakanov’s Formula. Journal of Mathematical Sciences and Applications. 2013; 1(2):36-38. doi: 10.12691/jmsa-1-2-5

Abstract

An algorithm for obtaining all n×n binary matrices having exactly 2 units in every row and every column is described in the paper. After analysing the work of the algorithm a formula for calculating the number of these matrices has been obtained. This formula is known and has been obtained using other methods, which by their nature are purely analytical and not constructive. Thus a new, constructive proof of this known formula has been obtained.

Keywords:
binary matrix algorithm constructive proof tarakanov’s formula

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References:

[1]	M. Aigner. Combinatorial Theori. Springer-Verlag, 1979.
[2]	P. Lancaster, Theory of Matrices. Academic Press, NY, 1969.
[3]	V. E. Tarakanov, Combinatorial problems on binary matrices. in Combinatorial Analysis, Vol. 5 (1980), Moscow State University, 4-15. (in Russian).