AbstractLet B(j, k; n) be the ordered set obtained by ordering the j element and k element subsets of an n element set by inclusion. We review results and proof techniques concerning the dimension dim(j, k; n) of B(j, k; n) for various ranges of the arguments j, k, and n
Extending a classical theorem of Sperner, we characterize the integers $m$ such that there exists a ...
AbstractA construction I(S) is defined which corresponds to the intuitive notion of the set of place...
Abstract(S, (⩽n)nϵN) is called an ordinal structure if S is a set and (⩽n)nϵN a family of quasi-orde...
AbstractLet B(j, k; n) be the ordered set obtained by ordering the j element and k element subsets o...
AbstractThe fractional dimension of an ordered set was introduced in Brightwell and Scheinerman (199...
A family F of s-subsets of [t]is a (ϑ,s,t)-family iff the intersection of any two distinct elements ...
This paper provides a new upper bound on the 2-dimension of partially ordered sets. The 2-dimension ...
AbstractA Boolean layer cake is an ordered set obtained from a Boolean lattice 2n by selecting any n...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1,…,n} ord...
AbstractIn this paper we reduce the intriguing conjecture dim(L)=o(|L|) for lattices to an extremal ...
Discrete MathematicsA partial order on subsets defined by inclusion is a Boolean algebra. Boolean al...
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and s...
AbstractThe dimension of a partially ordered set P is the smallest integer n (if it exists) such tha...
Let L be a finite lattice and let L ̂ = L − {0̂, 1̂}. It is shown that if the order complex ∆(L̂) s...
AbstractWe study the topic of the title in some detail. The main results are summarized in the first...
Extending a classical theorem of Sperner, we characterize the integers $m$ such that there exists a ...
AbstractA construction I(S) is defined which corresponds to the intuitive notion of the set of place...
Abstract(S, (⩽n)nϵN) is called an ordinal structure if S is a set and (⩽n)nϵN a family of quasi-orde...
AbstractLet B(j, k; n) be the ordered set obtained by ordering the j element and k element subsets o...
AbstractThe fractional dimension of an ordered set was introduced in Brightwell and Scheinerman (199...
A family F of s-subsets of [t]is a (ϑ,s,t)-family iff the intersection of any two distinct elements ...
This paper provides a new upper bound on the 2-dimension of partially ordered sets. The 2-dimension ...
AbstractA Boolean layer cake is an ordered set obtained from a Boolean lattice 2n by selecting any n...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1,…,n} ord...
AbstractIn this paper we reduce the intriguing conjecture dim(L)=o(|L|) for lattices to an extremal ...
Discrete MathematicsA partial order on subsets defined by inclusion is a Boolean algebra. Boolean al...
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and s...
AbstractThe dimension of a partially ordered set P is the smallest integer n (if it exists) such tha...
Let L be a finite lattice and let L ̂ = L − {0̂, 1̂}. It is shown that if the order complex ∆(L̂) s...
AbstractWe study the topic of the title in some detail. The main results are summarized in the first...
Extending a classical theorem of Sperner, we characterize the integers $m$ such that there exists a ...
AbstractA construction I(S) is defined which corresponds to the intuitive notion of the set of place...
Abstract(S, (⩽n)nϵN) is called an ordinal structure if S is a set and (⩽n)nϵN a family of quasi-orde...
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