Abstract
Let R(A) denote the row space of a Boolean matrix A of order n. We show that if n ≥7, then the cardinality |R(A)| ∉ (2n−1 - 2n−5, 2n−1 - 2n−6) U (2n−1 - 2n−6, 2n−1). This result confirms a conjecture in [1].
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AMS Subject Classification (1991): 05B20 06E05 15A36
Support partially by the Postdoctoral Science Foundation of China.
Dedicated to Professor Chao Ko on the occasion of his 90th birthday
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Hong, S. Distribution of Cardinalities of Row Spaces of Boolean Matrices of Order n. SEA bull. math. 24, 51–64 (2000). https://doi.org/10.1007/s10012-000-0051-4
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DOI: https://doi.org/10.1007/s10012-000-0051-4