# Slack matrices, k-products, and 2-level polytopes

@article{Aprile2021SlackMK, title={Slack matrices, k-products, and 2-level polytopes}, author={Manuel Aprile and Michele Conforti and Yuri Faenza and Samuel Fiorini and Tony Huynh and Marco Macchia}, journal={ArXiv}, year={2021}, volume={abs/2106.12829} }

In this paper, we study algorithmic questions concerning products of matrices and their consequences for recognition algorithms for polyhedra. The 1-product of matrices S1 ∈ R m1×n1 , S2 ∈ R m2×n2 is a matrix in R1212 whose columns are the concatenation of each column of S1 with each column of S2. The k-product generalizes the 1-product, by taking as input two matrices S1, S2 together with k − 1 special rows of each of those matrices, and outputting a certain composition of S1, S2. Our first…

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