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Showing 1 to 20 of 51 for “"Poset"”.
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Zero Divisor Graphs and Poset Decomposition
… some known results on zero-divisor graphs of posets as well as the concept of compactness as it relates to zero-divisor graphs. We will dicuss equivalence class graphs defined on the elements of various algebraic structures and also the reduced graph defined on the vertices of a compact graph. …
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Código MDS com a métrica POSET
… generalização da métrica de Hamming é a métrica poset. Faremos um estudo detalhado dos espaços poset, hierarquia de I-pesos e a I-distribuição de pesos, dando ênfase aos códigos poset não degenerados. Verificamos a relação de dualidade poset entre as hierarquias de um código e seu dual. Definimos …
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Poset saturation and other combinatorial results
… These results fall into four broad areas: poset saturation, Ramsey theory, pursuit and evasion, and union-closed families. Chapter 2 is dedicated to the area of poset saturation. Given a finite poset P, we call a family F of subsets of [n] P-saturated if F does not contain an induced copy …
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Permutations statistics of indexed and poset permutations
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1992.
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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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Edge Labelings on the Partially Ordered Set of Non-Crossing Bonds
… is known as an ER-labeling. We explore a new subposet of this lattice which we call the “non-crossing bond poset” for all graphs finite graphs. Then we aim to show when this subposet has the desired ER-labeling and when it does not. This paper will focus on what the bond lattice of a graph is, …
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A partial order approach to decentralized control
… We employ the theory of partially ordered sets (posets) to model and analyze a class of decentralized control problems. Posets have attractive combinatorial and algebraic properties; the combinatorial structure enables us to model a rich class of communication structures in systems, and the …
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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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Topics in the Generation of Ideals of Posets
… which contains as vertices the k-ideals of the poset P, with an edge between vertices that differ by a swap, has a Hamiltonian 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 …
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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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Painted Trees and Pterahedra
… bijection to tubings, that for <i>n</i> ≤ 4 the poset of the painted face trees with <i>n</i>+1 leaves is isomorphic to the face poset of an <i>n</i>-dimensional polytope, specifically KF<sub>1,<i>n</i></sub>, the graph-associahedron for a fan graph, F<sub>1,<i>n</i></sub>.
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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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The combinatorics of reduced decompositions
… zonotopal tilings of a particular polygon, and a poset defined in terms of these tilings. The class of freely braided permutations behaves particularly well, and its graphs and posets are explicitly determined. The Bruhat order for the symmetric group is examined, and the permutations with boolean …
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Extremal problems on counting combinatorial structures
… Sharifzadeh. In Chapte 4, we seek families in posets with the smallest number of comparable pairs. Given a poset $P$, a family $\F\subseteq P$ is \emph{centered} if it is obtained by `taking sets as close to the middle layer as possible'. A poset $P$ is said to have the \emph{centeredness …
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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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Combinatorics of acyclic orientations of graphs : algebra, geometry and probability
… linear extensions or topological sortings of a poset, from both the points of view of poset theory and enumerative combinatorics, and of the geometry of hyperplane arrangements and zonotopes. What can be said about the distribution of acyclic orientations obtained from a uniformly random …
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Some Extremal Problems on Graphs and Partial Orders
A unichain in a product poset P x Q is a chain in which the value of one coordinate is fixed. A semiantichain in P x Q is a family S such that (u, v) < ( u', v') for two elements of S only if u < u' and v < v' . Saks and West conjectured that for every product of partial orders, the maximum size of …
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Free resolutions, combinatorics, and geometry
… gives a module-theoretic interpretation of this poset structure. The study of the cone of cohomology tables over an arbitrary polarized projective variety is closely related to the existence of an Ulrich sheaf, and our second result shows that such sheaves exist on the class of Schubert …
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The combinatorics of adinkras
… Pfaffian orientations, graph coloring, and poset theory. Selected results include the enumeration of odd dashings for all adinkraizable chromotopologies, the notion of Stiefel-Whitney classes for codes and their vanishing conditions, and the enumeration of all Hamming cube adinkras up …
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Coloring and constructing (hyper)graphs with restrictions
… In Chapter 6 we consider a question concerning poset dimension. Dorais asked for the maximum guaranteed size of a subposet with dimension at most d of an n-element poset. A lower bound of sqrt(dn) was observed by Goodwillie. We provide a sublinear upper bound.
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