Partial Orders and Complexity: The Young Diagram Lattice

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.

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Modeling country risk ratings using partial orders

European Journal of Operational Research ◽

10.1016/j.ejor.2005.06.040 ◽

2006 ◽

Vol 175 (2) ◽

pp. 836-859 ◽

Cited By ~ 32

Author(s):

P.L. Hammer ◽

A. Kogan ◽

M.A. Lejeune

Keyword(s):

Country Risk ◽

Partial Orders

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Frequent Closed Partial Orders Mining in Sequences

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.846-847.1304 ◽

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.

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Convex Bodies, Graphs and Partial Orders

Proceedings of the London Mathematical Society ◽

10.1112/s0024611500012168 ◽

2000 ◽

Vol 80 (2) ◽

pp. 415-450 ◽

Cited By ~ 4

Author(s):

Bela Bollobas ◽

Graham R. Brightwel

Keyword(s):

Convex Bodies ◽

Partial Orders

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NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x1340006x ◽

2013 ◽

Vol 28 (03n04) ◽

pp. 1340006 ◽

Cited By ~ 88

Author(s):

OSCAR CHACALTANA ◽

JACQUES DISTLER ◽

YUJI TACHIKAWA

Keyword(s):

Lie Algebra ◽

Young Diagram ◽

Central Charge ◽

Outer Automorphism ◽

Natural Generalization ◽

Nilpotent Orbits ◽

Coulomb Branch ◽

Local Properties

We study the local properties of a class of codimension-2 defects of the 6d [Formula: see text] theories of type J = A, D, E labeled by nilpotent orbits of a Lie algebra [Formula: see text], where [Formula: see text] is determined by J and the outer-automorphism twist around the defect. This class is a natural generalization of the defects of the six-dimensional (6d) theory of type SU (N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the four-dimensional (4d) central charges a and c and to the flavor central charge k.

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