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Orders on Subsets Rationalised by Abstract Convex Geometries
Order - Tập 26 Số 3 - Trang 237-244 - 2009
κ-Complete Uniquely Complemented Lattices
Order - - 2008
We show that for any infinite cardinal κ, every complete lattice where each element has at most one complement can be regularly embedded into a uniquely complemented κ-complete lattice. This regular embedding preserves all joins and meets, in particular it preserves the bounds of the original lattice. As a corollary, we obtain that every lattice where each element has at most one complement can be......
The number of orders with thirteen elements
Order - Tập 9 - Trang 203-204 - 1992
The number of non-isomorphic posets on 13 elements is P13=33,823,827,452
An announcement of this result was sent to the on July 4th, 1992.
. This extends our previous result P12 which constituted the greatest known value. A table enumerates the posets according to their number of relations.
The Relationship of Partial Metric Varieties and Commuting Powers Varieties
Order - Tập 30 - Trang 403-414 - 2012
Holland et al. (Algebra Univers 67:1–18, 2012) considered varieties
${\mathcal E}_n$
of lattice-ordered groups defined by partial metrics, and showed for all n that
${\mathcal E}_n$
is contained within the vari......
Scheduling rooted forests with communication delays
Order - - 1994
We show that a greedy algorithm for scheduling unit time jobs on two machines with unit communication delays produces an optimal schedule when the precedence constraints are given by a rooted forest. We also give a min/max relationship for the length of such a schedule. The min/max result (for forests and two machines) shows that the addition of unit communication delays increases the optimal sche......
Order-Sensitive Domination in Partially Ordered Sets and Graphs
Order - Tập 40 - Trang 157-172 - 2022
For a (finite) partially ordered set (poset) P, we call a dominating set D in the comparability graph of P, an order-sensitive dominating set in P if either x ∈ D or else a < x < b in P for some a,b ∈ D for every element x in P which is neither maximal nor minimal, and denote by γos(P), the least size of an order-sensitive dominating set of P. For every graph G and integer
......
Cartesian Lattice Counting by the Vertical 2-sum
Order - Tập 39 - Trang 113-141 - 2021
A vertical 2-sum of a two-coatom lattice L and a two-atom lattice U is obtained by removing the top of L and the bottom of U, and identifying the coatoms of L with the atoms of U. This operation creates one or two nonisomorphic lattices depending on the symmetry case. Here the symmetry cases are analyzed, and a recurrence relation is presented that expresses the number of nonisomorphic vertical 2-......
The dimension of cycle-free orders
Order - Tập 9 - Trang 103-110 - 1992
The existence of a four-dimensional cycle-free order is proved. This answers a question of Ma and Spinrad. Two similar problems are also discussed.
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