127 research outputs found

    Dilworth rate: a generalization of Witsenhausen's zero-error rate for directed graphs

    Get PDF

    Strong Qualitative Independence

    Get PDF
    AbstractThe subsets A,B of the n-element X are said to be s-strongly separating if the two sets divide X into four sets of size at least s. The maximum number h(n,s) of pairwise s-strongly separating subsets was asymptotically determined by Frankl (Ars Combin. 1 (1976) 53) for fixed s and large n. A new proof is given. Also, estimates for h(n,cn) are found where c is a small constant

    Intersecting P-free families

    Get PDF
    We study the problem of determining the size of the largest intersecting P-free family for a given partially ordered set (poset) P. In particular, we find the exact size of the largest intersecting B-free family where B is the butterfly poset and classify the cases of equality. The proof uses a new generalization of the partition method of Griggs, Li and Lu. We also prove generalizations of two well-known inequalities of Bollobás and Greene, Katona and Kleitman in this case. Furthermore, we obtain a general bound on the size of the largest intersecting P-free family, which is sharp for an infinite class of posets originally considered by Burcsi and Nagy, when n is odd. Finally, we give a new proof of the bound on the maximum size of an intersecting k-Sperner family and determine the cases of equality. © 2017 Elsevier Inc

    Generalized forbidden subposet problems

    Get PDF

    On Structural Resource of Monotone Recognition

    Get PDF
    Algorithmic resources are considered for elaboration and identification of monotone functions and some alternate structures are brought, which are more explicit in sense of structure and quantities and which can serve as elements of practical identification algorithms. General monotone recognition is considered on multi- dimensional grid structure. Particular reconstructing problem is reduced to the monotone recognition through the multi-dimensional grid partitioning into the set of binary cubes

    On the number of minimal completely separating systems and antichains in a Boolean lattice

    Get PDF
    An (n)completely separating system C ((n)CSS) is a collection of blocks of [n] = {1,..., n} such that for all distinct a, b ∈ [n] there are blocks A, B ∈C with a ∈ A \ B and b ∈ B \ A. An (n)CSS is minimal if it contains the minimum possible number of blocks for a CSS on [n]. The number of non-isomorphic minimal (n)CSSs is determined for 11 ≤ n ≤ 35. This also provides an enumeration of a natural class of antichains
    corecore