3 problems

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The probabilistic lower-bound conjecture for invertible binary matrices
Let $R_t(s)$ denote the maximum proportion of invertible $2$ -by- $2$ submatrices among the relevant submatrices of an invertible binary matrix of size $s$ for parameter $t$ , and sup…
Conjectureopencombinatorial-matrix-theory finite-fields probabilistic-methodarXiv posted 2 days ago
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Polylogarithmic gaps conjecture for the 6-GP-free process
Let $T$ be the sequence generated by the $6$ -GP-free process, and interpret a gap of size $O((\log x)^C)$ as the existence of a constant implicit in the big- $O$ bound, independent…
Conjectureopengap-problems geometric-progressions probabilistic-methodarXiv posted 2 days ago
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The conjecture on the universal lower bound for maximal determinants
Universal lower-bound conjecture. The condition that $n$ be sufficiently large can be omitted: the inequality
Conjectureopenhadamard-matrices maximal-determinants probabilistic-methodarXiv posted 2 days ago

The probabilistic lower-bound conjecture for invertible binary matrices