The fractional binary rank is not multiplicative under Kronecker products: the Domino matrix gives bpf(D⊗D) ≤ 6 < 6.25, and its asymptotic fractional rank lies between 2 and 2.373.
On biclique cover and partition problems
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Engineering Insights into Biclique Partitions and Fractional Binary Ranks of Matrices
The fractional binary rank is not multiplicative under Kronecker products: the Domino matrix gives bpf(D⊗D) ≤ 6 < 6.25, and its asymptotic fractional rank lies between 2 and 2.373.