ON THE STABILIZATION OF THE NUMBER OF ORBITS OF HIGH-RANK CAMERON MATRICES
Abstract
A quadratic (0,1)-matrix of degree n with just n units among its elements will be called a Cameron matrix. The orbits of the natural action of the group Sn× Sn (the square of the symmetric group of degree n) on the set of Cameron matrices of degree n (an independent action on the rows and the columns of matrices) are considered. It is proved that for fixed d < n, the number of such orbits for matrices of rank n – d is constant for n ≥ 3d and grows with the growth of n if n < 3d. For each orbit, its representative in a quasi-Jordan form is indicated.
About the Authors
V. A. Lipnitski
Military Academy of the Republic of Belarus
Belarus
D. Sc. (Engineering), Professor, Head of the Department of Mathematics
Belarus
D. Sc. (Engineering), Professor, Head of the Department of Mathematics
A. I. Sergey
Yanka Kupala State University of Grodno
Belarus
Postgraduate
Belarus
Postgraduate
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