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Showing 1 to 16 of 16 for “"partially ordered set"”.
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Edge Labelings on the Partially Ordered Set of Non-Crossing Bonds
Let G be a graph with a finite vertex set and edge set. A bond of G is a spanning subgraph of G whose connected components are induced. This collection of bonds form a partially ordered set which is also a lattice. This lattice has what is known as an ER-labeling. We explore a new subposet of this …
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Group automorphisms of incidence algebras.
Let (P,≤) be an arbitrary partially ordered set and I(P) its incidence space. Then FI(P) denotes the associated finitary incidence algebra, where FI(P) = I(P) for locally finite posets (P,≤). We investigate the group of units U(FI(P)) of incidence algebras and its normal subgroups. This includes …
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A Combinatorial View of Weighted Voting
Given a chain of the partially ordered set of weighted games, it is currently unknown if weights can be assigned to each of the $n$ voters so that the chain is weighted. We conjecture that every consistent chain $C$ through weighted games admits weights, $\vec{w}$, such that for all weighted games …
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Problems and results in partially ordered sets, graphs and geometry
… the height sequence of an element of a partially ordered set. Let $x$ be an element of the partially ordered set $P$. Then $h_i(x)$ is the number of linear extensions of $P$ in which $x$ is in the $i$th lowest position. The sequence ${h_i(x)}$ is called the height sequence of $x$ in $P$. …
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Anti-Unification in Constraint Logics: Foundations and Applications to Learnability in First-Order Logic, to Speed-Up Learning, and to Deduction
… of any two or more syntactic objects in a partially-ordered set of such objects. The dual of unification is an operation called generalization, or anti-unification, which computes least or minimal upper bounds. As with unification, anti-unification comes in a variety of forms. The thesis of …
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Hyperconvexity and endpoints in T₀-quasi-metric spaces
… spaces are presented. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and the q-hyperconvex hull of its natural T₀-quasi-metric space.
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Extremal Problems On Families of Subsets With Forbidden Subposets
<p>We study the families of subsets of finite sets that have some special properties. For all families with the properties, we look for the largest sizes of the families. In the thesis, we use a method to bound the size of families of subsets, which is what we call the Lubell function now. The …
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The Quicksort algorithm and related topics
… advance. We discuss a number of cases where the partially ordered sets arise at random. To this end, we employ results from Graph and Information Theory. Finally, we obtain an alternative bound on the number of linear extensions when the partially ordered set arises from a random graph, and …
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A Theory of Stationary Trees and the Balanced Baumgartner-Hajnal-Todorcevic Theorem for Trees
… height. We define the diagonal union of subsets of a tree, as well as normal ideals on a tree, and we characterize arbitrary subsets of a non-special tree as being either stationary or non-stationary. We then use this theory to prove the following partition relation for trees: Main Theorem. …
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Taskmaster: an interactive, graphical environment for task specification, execution and monitoring
… consists of decomposing the problem task into a partially ordered set of high-level subtasks. This decomposition is depicted graphically as a network in which the nodes correspond to the subtasks and the arcs represent the directed data paths between the nodes. The subtasks are successively …
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Combinatorial channels from partially ordered sets
… classical and modern, using the framework of partially ordered sets. We represent adversarial error models as combinatorial channels, form combinatorial channels from posets, identify a structural property of posets that leads to families of channels with the same codes, and bound the size of …
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Quasireflections and quasifactorizations
… of their ideas are extended to the more general setting of quasireflections (Bargenda 94]. In particular, one would like to view the well-known concept of an injective hull as a "completion", and this can be accomplished via a Galois correspondence between such hulls on one hand, and …
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Arrangement of minors in the positive Grassmannian
… of largest value are in bijection with sorted sets, which earlier appeared in the context of alcoved polytopes and Gröbner bases. Maximal arrangements of this form correspond to simplices of the alcoved triangulation of the hypersimplex; and the number of such arrangements equals the Eulerian …
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Similarity Assessment and Retrieval of CAD Models
… design precedence semantics are organized as a partially ordered set (POSET). Two knowledge-driven FDAG partitioning schemes have been proposed to extract reusable CAD components. With these partitionings applied on existing CAD models, the CAD model similarity is no longer assessed on rigid 3D …
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Combinatorial aspects of synchronisation, percolation, and arithmetic
… the same phase, for every initial state up to a set of measure zero. We show that if $\varepsilon > 0$ and $p \geq (1 + \varepsilon)(\log n)/n$, then the Kuramoto model on the Erdős-Rényi graph $G(n,p)$ is globally synchronising with probability tending to one as $n$ goes to infinity. This …
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On the Formal Flexibility of Syntactic Categories
… in human language are necessarily totally ordered, as certain analytical devices (e.g., "flavored" categories) can only be theoretically maintained if we also allow categorial sequences to be partially ordered. After a diachronic study of the flavored verbalizer $v_{BE}$ (stative) in …