Abstract

The discriminantal arrangement $\mathcal{ℬ}(n,k,\mathcal{𝒜})$ is an arrangement of hyperplanes constructed from a generic arrangement $\mathcal{𝒜}$ of $n$ hyperplanes in a $k$-dimensional space generalizing the classical braid arrangement. In this paper, we tie the combinatorics of the discriminantal arrangement $\mathcal{ℬ}(n,k,\mathcal{𝒜})$ with the well-known generalized Sylvester’s and orchard problems and we present an example which shows how this connection could be useful to address those two problems.

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