In this paper, we introduce the notion of β-greedoids and discuss four basic constructions of β -greedoids namely, deletion, contraction, direct sum and ordered sum. We show that the operations of deletion and contraction commute and the direct sum and ordered sum of β-greedoids G 1 and G 2 are interval β-greedoids if and only if G 1 and G 2 are both interval β-greedoids. We also give a necessary and su.cient condition for the direct sum and ordered sum of balanced β -greedoids to be balanced.
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