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Let $M$ be a $0/1$ matrix over $\mathbb F_2^{n\times n}$ with determinant $0$. The set of such singular matrices form a semigroup. The set of nilpotent matrices of size $n\times n$ form a semigroup. ...

I'm trying to read this paper, Total positivity, Grassmannians and networks by Postnikov (https://arxiv.org/abs/math/0609764) and I'm stuck on Lemma 5.1, which is essentially an identity about maximal ...

Conjecture: Let $e_1 = (1,0,\ldots,0), \ldots , e_{m_1+m_2} = (0,\ldots,0,1)$ be the unit vectors of the standard basis $E$ of $\mathbb{R}^{m_1+m_2}$. An enumeration $ E \cup -E = \{f_1, \ldots, ...