منابع مشابه
Q 2-free Families in the Boolean Lattice
For a family F of subsets of [n] = {1, 2, . . . , n} ordered by inclusion, and a partially ordered set P , we say that F is P -free if it does not contain a subposet isomorphic to P . Let ex(n, P ) be the largest size of a P -free family of subsets of [n]. Let Q2 be the poset with distinct elements a, b, c, d, a < b, c < d; i.e., the 2-dimensional Boolean lattice. We show that 2N − o(N) ≤ ex(n,...
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The Boolean lattice of dimension two, also known as the diamond, consists of four distinct elements with the following property: A ⊂ B,C ⊂ D. A diamondfree family in the n-dimensional Boolean lattice is a subposet such that no four elements form a diamond. Note that elements B and C may or may not be related. There is a diamond-free family in the n-dimensional Boolean lattice of size (2−o(1)) (...
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In this paper I construct lattice models with an underlying U q osp(2, 2) su-peralgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These trigonometric R-matrices depend on three continuous parameters, the spectral parameter, the deformation parameter q and the U (1) parameter, b, of the superalgebra. It must be emphasized that the parameter q is generic and the parameter...
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Let p be a positive integer and let Q be a subset of {0, 1, . . . , p}. Call p sets A1, A2, . . . , Ap of a ground set X a (p,Q)-system if the number of sets Ai containing x is in Q for every x ∈ X. In hypergraph terminology, a (p,Q)-system is a hypergraph with p edges such that each vertex x has degree d(x) ∈ Q. A family of sets F with ground set X is called (p,Q)-free if no p sets of F form a...
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ژورنال
عنوان ژورنال: Order
سال: 2011
ISSN: 0167-8094,1572-9273
DOI: 10.1007/s11083-011-9206-4