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Showing 1 to 5 of 5 for “"Boolean Lattice"”.
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Universal Cycles for Some Combinatorial Objects
… to the sets in any labeled subposet of the Boolean lattice; de Bruijn's theorem corresponds to the case when the subposet in question consists of a single ground element. In this paper, we also show that de Bruijn's cycles exist for words with weight between <em>s</em> and<em> t</em>, where …
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Classification and enumeration of special classes of posets and polytopes
… by the work of R. Stanley about recognizing the boolean lattice by looking at smaller intervals. In the second topic concerns lattice path matroid polytopes. The theory of matroid polytopes has gained prominence due to its applications in algebraic geometry, combinatorial optimization, Coxeter …
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Combinatorial Problems with Geometric Flavour
… (convex set intersected with an affine sub-lattice) containing $A$. In particular, we deduce the sharp stability result for the Brunn--Minkowski inequality for equal sets, conjectured by Figalli and Jerison. Given $\delta>0$ sufficiently small and $A\subset \mathbb{R}^k$ with $|A+A|\le …
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Problems and results in partially ordered sets, graphs and geometry
… second kind. In the third part, we consider the lattice whose elements are the subsets of ${1,2,ldots,n}$. Trotter and Felsner asked whether this subset lattice always contains a monotone Hamiltonian path. We make progress toward answering this question by constructing a path for all $n$ that …
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Extremal problems on counting combinatorial structures
… of comparable pairs. Kleitman showed that the Boolean lattice $\{0,1\}^n$ has the centeredness property. It was conjectured by Noel, Scott, and Sudakov, and by Balogh and Wagner, that the poset $\{0,1,\ldots,k\}^n$ also has the centeredness property, provided $n$ is sufficiently large compared …