scholarly journals True cofinality and bounding number for small products of partial orders

2003 ◽  
Vol 122 (1-3) ◽  
pp. 87-106
Author(s):  
Stefan Neumann
Keyword(s):  
Partial Orders

THE NATURAL PARTIAL ORDER ON LINEAR SEMIGROUPS WITH NULLITY AND CO-RANK BOUNDED BELOW

2014 ◽  
Vol 91 (1) ◽  
pp. 104-115 ◽  
Author(s):  
SUREEPORN CHAOPRAKNOI ◽  
TEERAPHONG PHONGPATTANACHAROEN ◽  
PONGSAN PRAKITSRI
Keyword(s):  
Semigroup Forum ◽  
Partial Order ◽  
Lower Bounds ◽  
Partial Orders ◽  
Natural Partial Order ◽  
Linear Transformations ◽  
Bounded Below

AbstractHiggins [‘The Mitsch order on a semigroup’, Semigroup Forum 49 (1994), 261–266] showed that the natural partial orders on a semigroup and its regular subsemigroups coincide. This is why we are interested in the study of the natural partial order on nonregular semigroups. Of particular interest are the nonregular semigroups of linear transformations with lower bounds on the nullity or the co-rank. In this paper, we determine when they exist, characterise the natural partial order on these nonregular semigroups and consider questions of compatibility, minimality and maximality. In addition, we provide many examples associated with our results.

Modeling country risk ratings using partial orders

2006 ◽  
Vol 175 (2) ◽  
pp. 836-859 ◽  
Author(s):  
P.L. Hammer ◽  
A. Kogan ◽  
M.A. Lejeune
Keyword(s):  
Country Risk ◽  
Partial Orders

Frequent Closed Partial Orders Mining in Sequences

2013 ◽  
Vol 846-847 ◽  
pp. 1304-1307
Author(s):  
Ye Wang ◽  
Yan Jia ◽  
Lu Min Zhang
Keyword(s):  
Sequence Data ◽  
Real Data ◽  
Partial Orders ◽  
Hard Problem ◽  
Important Data ◽  
Data Set ◽  
Pruning Algorithm ◽  
Equal Chance ◽  
Np Hard Problem ◽  
General Sequences

Mining partial orders from sequence data is an important data mining task with broad applications. As partial orders mining is a NP-hard problem, many efficient pruning algorithm have been proposed. In this paper, we improve a classical algorithm of discovering frequent closed partial orders from string. For general sequences, we consider items appearing together having equal chance to calculate the detecting matrix used for pruning. Experimental evaluations from a real data set show that our algorithm can effectively mine FCPO from sequences.

Convex Bodies, Graphs and Partial Orders

2000 ◽  
Vol 80 (2) ◽  
pp. 415-450 ◽  
Author(s):  
Bela Bollobas ◽  
Graham R. Brightwel
Keyword(s):  
Convex Bodies ◽  
Partial Orders

Cycle-free partial orders and chordal comparability graphs

Order ◽  
1991 ◽  
Vol 8 (1) ◽  
pp. 49-61 ◽  
Author(s):  
Tze-Heng Ma ◽  
Jeremy P. Spinrad
Keyword(s):  
Partial Orders

A model in partial orders for comparing objects by dualistic measures

1986 ◽  
Vol 78 (2) ◽  
pp. 179-192 ◽  
Author(s):  
William H.E. Day ◽  
Daniel P. Faith
Keyword(s):  
Partial Orders

scholarly journals Maximal elements under the three partial orders

1992 ◽  
Vol 175 ◽  
pp. 39-61 ◽  
Author(s):  
Robert E. Hartwig ◽  
Raphael Loewy
Keyword(s):  
Partial Orders ◽  
Maximal Elements

Natural Partial Orders

1968 ◽  
Vol 20 ◽  
pp. 535-554 ◽  
Author(s):  
R. A. Dean ◽  
Gordon Keller
Keyword(s):  
Partial Orders ◽  
Partial Ordering ◽  
Finite Set ◽  
Partial Orderings

Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering. This is a consequence of the theorem of Szpielrajn (5) which states that every partial ordering of a set may be refined to a total ordering. In this paper we consider only natural partial orderings. In the first section we obtain theorems about the lattice of all NPO's of T(n).

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