Results 1  10
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170
On the Metric Dimension of Cartesian Products of Graphs
"... A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Using bounds on the order of the so called doubly resolving sets, we establish bounds on G�H ..."
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Cited by 70 (5 self)
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A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Using bounds on the order of the so called doubly resolving sets, we establish bounds on G
of Products of Posets
"... In this note we give a description of the representation of the wreath product Sn[G] of the symmetric group Sn and a finite group G on the homology of the product of n copies of a partially ordered set (poset for short) P on which G acts as a group of automorphisms. In the sequel all posets will be ..."
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will be finite. We will consider three types of product constructions. The direct product P ×Q of two posets P and Q is the poset on the Cartesian product P ×Q whose order relation is defined by (x, y) ≤ (x ′ , y ′ ) if and only if x ≤ x ′ in P and y ≤ y ′ in Q. In case a poset P contains a least element ˆ0, we
Packing Dimension and Cartesian Products
, 1996
"... We show that for any analytic set A in R d , its packing dimension dim P (A) can be represented as sup B fdim H (A B) dim H (B)g ; where the supremum is over all compact sets B in R d , and dim H denotes Hausdorff dimension. (The lower bound on packing dimension was proved by Tricot in 1982) ..."
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We show that for any analytic set A in R d , its packing dimension dim P (A) can be represented as sup B fdim H (A B) dim H (B)g ; where the supremum is over all compact sets B in R d , and dim H denotes Hausdorff dimension. (The lower bound on packing dimension was proved by Tricot in 1982
ON SCATTERED POSETS WITH FINITE DIMENSION
, 812
"... Abstract. We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains. Introduction and presentation of the results A fundamental result, due to Szpilrajn [26], states that every order on a set is the int ..."
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Abstract. We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains. Introduction and presentation of the results A fundamental result, due to Szpilrajn [26], states that every order on a set
A Posetal Cartesian DoublyClosed Category
, 2006
"... We describe a poset which has the structure of a Cartesian doublyclosed category, and is therefore a categorical model of BI, O’Hearn and Pym’s Logic of Bunched Implications [1], albeit a very degenerate one. 1 A posetal CDCC Consider the poset (N, ≥), i.e. the natural numbers ordered by the greater ..."
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We describe a poset which has the structure of a Cartesian doublyclosed category, and is therefore a categorical model of BI, O’Hearn and Pym’s Logic of Bunched Implications [1], albeit a very degenerate one. 1 A posetal CDCC Consider the poset (N, ≥), i.e. the natural numbers ordered
On Posets whose Products are Macaulay
, 1998
"... If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs have the same length. ..."
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If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs have the same length.
Combinatorial dimension of fractional Cartesian products
 Proc. Amer. Math. Soc
, 1994
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 3 (1 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
THE POSET OF BIPARTITIONS
, 2009
"... Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on bipartitional relations given by inclusion. We show that, with r ..."
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Cited by 2 (0 self)
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, with respect to this partial order, the bipartitional relations on a set of size n form a graded lattice of rank 3n − 2. Moreover, we prove that the order complex of this lattice is homotopy equivalent to a sphere of dimension n − 2. Each proper interval in this lattice has either a contractible order complex
Bounds on the kdimension of products of special posets
, 2008
"... Trotter conjectured that dim P × Q ≥ dimP + dim Q − 2 for all posets P and Q. To shed light on this, we study the kdimension of products of finite orders. For fixed k, the value 2 dimk (P) − dimk (P × P) is unbounded when P is an antichain, and 2 dim2 (mP) − dim2 (mP × mP) is unbounded when P is ..."
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Cited by 1 (1 self)
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Trotter conjectured that dim P × Q ≥ dimP + dim Q − 2 for all posets P and Q. To shed light on this, we study the kdimension of products of finite orders. For fixed k, the value 2 dimk (P) − dimk (P × P) is unbounded when P is an antichain, and 2 dim2 (mP) − dim2 (mP × mP) is unbounded when P
Results 1  10
of
170