Orientable arithmetic matroids

TL;DR

This paper introduces the concept of orientable arithmetic matroids, extending the theory of matroids to include orientation, and proves fundamental properties such as the uniqueness of orientation.

Contribution

It defines the new concept of oriented arithmetic matroids and establishes key properties, advancing the theoretical framework of matroid generalizations.

Findings

Defined the concept of oriented arithmetic matroids

Proved the uniqueness of orientation property

Extended matroid theory to include orientation aspects

Abstract

The theory of matroids has been generalized to oriented matroids and, recently, to arithmetic matroids. We want to give a definition of "oriented arithmetic matroid" and prove some properties like the "uniqueness of orientation".