Dmitry N. Kozlov

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To every directed graph G one can associate a complex (G) consisting of directed subforests. This construction, suggested to us by R. Stanley, is especially important in the case of a complete double directed graph Gn, where it leads to studying some interesting representations of the symmetric group and corresponds (via Stanley-Reisner correspondence) to(More)
Let ∆(Πn) denote the order complex of the partition lattice. The natural Sn-action on the set [n] induces an Sn-action on ∆(Πn). We show that the regular CW complex ∆(Πn)/Sn is collapsible. Even more, we show that ∆(Πn)/Sn is collapsible, where Π∆ is a suitable type selection of the partition lattice. This allows us to generalize and reprove in a conceptual(More)
For positive integers n and d, and the probability function 0 ≤ p(n) ≤ 1, we let Yn,p,d denote the probability space of all at most d-dimensional simplicial complexes on n vertices, which contain the full (d − 1)-dimensional skeleton, and whose d-simplices appear with probability p(n). In this paper we determine the threshold function for vanishing of the(More)
In this paper we study implications of folds in both parameters of Lovász’ Hom(−,−) complexes. There is an important connection between the topological properties of these complexes and lower bounds for chromatic numbers. We give a very short and conceptual proof of the fact that if G− v is a fold of G, then bdHom(G,H) collapses onto bdHom(G − v,H), whereas(More)
Given a set of m coins out of a collection of coins of k unknown distinct weights, we wish to decide if all the m given coins have the same weight or not using the minimum possible number of weighings in a regular balance beam. Let m(n, k) denote the maximum possible number of coins for which the above problem can be solved in n weighings. We show that m(n,(More)