Some results on vertices of integer partition polytopes
Shlyk V. A.
"Математика. Компьютер. Образование". Cб. трудов XV международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2008. Vol. 2, 276pp. Pp. 91-98. (accepted)
In 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
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