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Showing 1 to 20 of 46 for “"Posets"”.
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Differential posets and dual graded graphs
In this thesis I study r-differential posets and dual graded graphs. Differential posets are partially ordered sets whose elements form the basis of a vector space that satisfies DU-UD=rI, where U and D are certain order-raising and order-lowering operators. New results are presented related to the …
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Simplicial posets--f-vectors and free resolutions
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991.
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Topics in the Generation of Ideals of Posets
… path. The conjecture is true for series-parallel posets and interval orders. We prove the conjecture also holds for the fence posets, but that the conjecture is false for the 3-ideals of the crown poset with six elements. We also provide an infinite family of posets for which the conjecture does …
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The annihilation graphs of commutator posets and lattices
We propose a new, widely generalized context for the study of the zero-divisor/ annihilating-ideal graphs, where the vertices of graphs are not elements/ideals of a commutative ring, but elements of an abstract ordered set (imitating the lattice of ideals), equipped with a binary operation …
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Kac's random walk and coupon collector's process on posets
… We refine these bounds for special classes of posets. For instance, we show the cut-off phenomenon for shallow posets that are closely connected to the classical Dixie Cup problem. We also prove the linear growth of the expectation for posets whose number of chains grows at most exponentially …
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Classification and enumeration of special classes of posets and polytopes
… and enumerative aspects of different classes of posets and polytopes. The first part concerns the finite Eulerian posets which are binomial, Sheffer or triangular. These important classes of posets are related to the theory of generating functions and to geometry. Ehrenborg and Readdy [ER2] gave …
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Chain and antichain enumeration in posets, and b-ary partitions
… known about the partition [lambda](P) for most posets P. Our first goal is to develop a method for calculating values of [lambda]k(P) for certain posets. We find the size of the largest union of two or three chains in the lattice of partitions of n under dominance order, and in the Tamari …
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Problems of optimal choice on posets and generalizations of acyclic colourings
… with ‘c’-tuplets. I shall move away from known posets in Chapter 3, assuming instead that the candidates come from a poset about which the only information known is its size and number of maximal elements. I shall show that, given this information, there is an algorithm that is successful with …
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Applications and extensions of Fomin's generalization of the Robinson-Schensted correspondence to differential posets
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991.
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The Smarandache vertices of the annihilation graphs of commutator posets and lattices with respect to an element and an ideal
… the algebraic properties of the commutator posets and lattices and their associated annihilation graphs with respect to an element [resp. an ideal] using the notion of the Smarandache vertices. Actually, AGz(L) (the annihilation graph of the commutator poset [lattice] L with respect to an …
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Extremal Problems On Families of Subsets With Forbidden Subposets
… forbidden poset(partially ordered set) for many posets and prove that these posets satisfy a conjecture of Griggs and Lu. On the other hand, we give the new proofs of the old results on this type of problems using the Lubell function method, which greatly shorten those proofs.</p> <p>In addition, …
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Decomposition of Certain Representations Into A Direct Sum of Indecomposable Representations
Representations of quivers and posets are produced by persistent homology. It is possible to decompose such representations into direct sums of indecomposable representations. The indecomposable representations of quivers and posets that arise from one dimensional persistent homology are well …
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Two Problems in Computational Genomics
… is inferring horizontal gene transfer using posets. We define these two problems and present algorithmic approaches for solving them. For the whole genome alignment, we define alignment graphs for representing different evolutionary events, and define a scoring function for those graphs. The …
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Topics in combinatorics and combinatorial algorithms
… structural parameter for partially ordered sets (posets). The parameter that we study is the interval number of a poset, denoted by i(P) for a poset P. The interval number is related to a well-studied poset parameter, partial order dimension. We derive an upper bound on the interval number of a …
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Interval order enumeration
… used to identify a statistic on the factorial posets of Claesson and Linusson (2011) following the Fishburn distribution. Factorial posets mapped to zero by this statistic are canonically labeled factorial posets which may alternatively be viewed as unlabeled interval orders. As a consequence …
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Edge labellings of partially ordered sets
… elements. We next study finite graded bounded posets that have Sn EL-labellings and describe a type A 0-Hecke algebra action on their maximal chains. This action is local and the resulting representation of these Hecke algebras is closely related to the flag h-vector. We show that finite graded …
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Combinatorial channels from partially ordered sets
… 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 codes by optimizing over a family of equivalent channels. A large number of previously studied coding problems that fit …
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Contributions on secretary problems, independent sets of rectangles and related problems
… of jumps is NP-hard even for chordal bipartite posets. For the class of posets having two directional orthogonal ray comparability graphs, we show that this problem is equivalent to finding a maximum independent set of a well-behaved family of rectangles. Using this, we devise combinatorial and …
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