Goran Kilibarda

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The problem of enumeration of m-antichains of k-bounded multisets on an n-set is considered. A formula for calculating the cardinality of the corresponding family in terms of the graph theory was obtained. A more general case of multiantichains is also considered. As an illustration the corresponding explicit formulas are given for the case when 1 ≤ m ≤ 4,(More)
For inorganic semiconductors crystalline order leads to a band structure which gives rise to drastic differences to the disordered material. An example is the presence of an indirect band gap. For organic semiconductors such effects are typically not considered, since the bands are normally flat, and the band-gap therefore is direct. Herein we show results(More)
An antichain is here regarded as a hypergraph that satisfies the following property: neither of every two different edges is a subset of the other one. The paper is devoted to the enumeration of antichains given on an n-set and having one or more of the following properties: being labeled or unlabeled; being ordered or unordered; being a cover (or a proper(More)
It is shown that every automaton acceptable for rectangular labyrinths can be reduced to an automaton that behaves according to either the left-hand rule or the right-hand rule, or does not move at all, in every plane rectangular labyrinth without leaves. This enables us to approach certain fundamental problems of the theory of automata in labyrinths in a(More)
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