Abstract
An asymptotic formula for the minimum possible number of even p × q submatrices of an m × n 0–1 matrix A is obtained. It is shown that if A is considered random and pq is even, then the distribution of the number of the even p × q submatrices of A is highly skewed to the right, the left endpoint of the distribution being very close to its mean, while its right endpoint is twice the mean. A relation to Turn numbers is indicated.
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References
D. de Caen, D. L. Kreher, and J. Wiseman, On constructive upper bounds for the Turn numbers T(n, 2r + 1, 2r), Congressus Numerantum, Vol. 65 (1988) pp. 277–280.
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A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Volume 1, Gordon and Breach Science Publishers, Amsterdam (1986).
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Communicated by: D. Jungnickel
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Pinelis, I. On the minimal number of even submatrices of 0–1 matrices. Des Codes Crypt 9, 85–93 (1996). https://doi.org/10.1007/BF00169777
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DOI: https://doi.org/10.1007/BF00169777
Keywords
- matrices
- random matrices
- even submatrices
- Turn numbers