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Conference publicationsSome results on vertices of integer partition polytopesIn this paper, we present some results on the vertices of integer partition polytopes with attention focused at the problem of recognising them. A criterion of representability of a given partition as a convex combination of two others, as well as sufficient and, separately, necessary conditions for a partition to be a vertex are presented. We introduce two combinatorial operations on partitions and show that all vertices of any integer partition polytope can be recursively generated with help of these operations from a considerably smaller subset of its support vertices |
