$\beta$-greedoids

Abstract

In this paper, we introduce the notion of $\beta$-greedoids and discussfour basic constructions of $\beta$-greedoids namely, deletion,contraction, direct sum and ordered sum. We show that the operations of deletionand contraction commute and the direct sum and ordered sum of $\beta$-greedoids$G_{1}$ and $G_{2}$ are interval $\beta$-greedoids if and only if$G_{1}$ and $G_{2}$ are both interval $\beta$-greedoids. We also give anecessary and sufficient condition for the direct sum and ordered sum ofbalanced $\beta$-greedoids to be balanced.