The generalized Sylvester’s and orchard problems via discriminantal arrangement

The discriminantal arrangement $ℬ (n, k, 𝒜)$ is an arrangement of hyperplanes constructed from a generic arrangement $𝒜$ of $n$ hyperplanes in a $k$ -dimensional space generalizing the classical braid arrangement. In this paper, we tie the combinatorics of the discriminantal arrangement $ℬ (n, k, 𝒜)$ 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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Keywords

discriminantal arrangements, intersection lattice, orchard problem, Sylvester's problem, line arrangements, non-very generic arrangements

Mathematical Subject Classification

Primary: 05B35, 14M15, 52C35

Milestones

Received: 23 May 2023

Revised: 17 May 2024

Accepted: 31 May 2024

Published: 25 July 2024

Authors

Pragnya Das
Department of Mathematics Hokkaido University Sapporo Japan

Elisa Palezzato
Department of Mathematics Hokkaido University Sapporo Japan

Simona Settepanella
Department of Economics and Statistics University of Turin Turin Italy

Vol. 21, No. 1, 2024

Pragnya Das, Elisa Palezzato and Simona Settepanella

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors