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Commutativity Preservers of Incidence Algebras
Let I ( X , K ) be the incidence algebra of a finite connected poset X over a field K and D ( X , K ) its subalgebra consisting of diagonal elements. We...
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Random bipartite posets and extremal problems
Previously, Erdős, Kierstead and Trotter [5] investigated the dimension of random height 2 partially ordered sets. Their research was motivated...
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Dilworth's decomposition theorem for posets in
ZF In set theory without the Axiom of Choice (
AC ), we investigate the set-theoretic strength of Dilworth’s theorem for infinite posets with finite... -
On the minimal cover property and certain notions of finite
In set theory without the axiom of choice, we investigate the deductive strength of the principle “every topological space with the minimal cover...
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A proof of Frankl’s union-closed sets conjecture for dismantlable lattices
In this paper, we prove Frankl’s Union-Closed Sets Conjecture for the class of dismantlable lattices, a more general class than the class of planar...
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A Lattice Path Interpretation of the Diamond Product
The diamond product is the poset operation that when applied to the face lattices of two polytopes results in the face lattice of the Cartesian...
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On structural decompositions of finite frames
A frame in an n -dimensional Hilbert space H n is a possibly redundant collection of vectors { f i } i ∈ I that span the space. A tight frame is a...
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On Weak Chromatic Polynomials of Mixed Graphs
A mixed graph is a graph with directed edges, called arcs , and undirected edges. A k -coloring of the vertices is proper if colors from {1, 2, . . . , k ...
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Homomorphic Image Orders on Combinatorial Structures
Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we...
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A Theory of Stationary Trees and the Balanced Baumgartner–Hajnal–Todorcevic Theorem for Trees
Building on early work by Stevo Todorcevic, we develop a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal...
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A 2-element antichain that is not contained in any finite retract
We give an example of an ordered set P which contains a 2-element antichain that is not contained in any finite retract of P .
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Computing maximal chains
In (Fund Math 60:175–186
1967 ), Wolk proved that every well partial order (wpo) has a maximal chain; that is a chain of maximal order type. (Note... -
Cubical Subdivisions and Local h-Vectors
Face numbers of triangulations of simplicial complexes were studied by Stanley by use of his concept of a local h -vector. It is shown that a parallel...
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Level Eulerian Posets
The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite...