New Transactions on Computers Essential Sets Available

2011 ◽  
Vol 10 (12) ◽  
pp. 1804-1804
Keyword(s):  
Essential Sets

scholarly journals Diagrams and Essential Sets for Signed Permutations

10.37236/8106 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
David Anderson
Keyword(s):  
Schubert Variety ◽  
Signed Permutation ◽  
Signed Permutations ◽  
Degeneracy Locus ◽  
Essential Set ◽  
Diagrammatic Method ◽  
Essential Sets ◽  
Rank Conditions ◽  
Theoretic Version

We introduce diagrams and essential sets for signed permutations, extending the analogous notions for ordinary permutations.  In particular, we show that the essential set provides a minimal list of rank conditions defining the Schubert variety or degeneracy locus corresponding to a signed permutation.  Our essential set is in bijection with the poset-theoretic version defined by Reiner, Woo, and Yong, and thus gives an explicit, diagrammatic method for computing the latter.

A note on minimal essential sets

1971 ◽  
Vol 18 (5) ◽  
pp. 557-560 ◽  
Author(s):  
G. Guardabassi
Keyword(s):  
Essential Sets

A note on minimal and quasi-minimal essential sets in complex directed graphs

1972 ◽  
Vol 19 (5) ◽  
pp. 512-513 ◽  
Author(s):  
M. Diaz ◽  
J. Richard ◽  
M. Courvoisier
Keyword(s):  
Directed Graphs ◽  
Essential Sets

On Essential Sets of Fixed Points for Functions

2015 ◽  
Vol 36 (7) ◽  
pp. 942-950 ◽  
Author(s):  
Q. Q. Song
Keyword(s):  
Fixed Points ◽  
Essential Sets

New Transactions on Computers Essential Sets Available

2011 ◽  
Vol 60 (10) ◽  
pp. 1520-1520
Keyword(s):  
Essential Sets

scholarly journals Computing Essential Sets for Convex and Non-convex Scenario Problems: Theory and Application

2021 ◽  
pp. 1-1
Author(s):  
Xinbo Geng ◽  
Le Xie ◽  
M. Sadegh Modarresi
Keyword(s):  
Essential Sets

scholarly journals Essential sets of Picard principle for rotation free densities

1991 ◽  
Vol 14 (1) ◽  
pp. 134-143
Author(s):  
Toshimasa Tada
Keyword(s):  
Essential Sets

scholarly journals Rough sets in graphs using similarity relations

2022 ◽  
Vol 7 (4) ◽  
pp. 5790-5807
Author(s):  
Imran Javaid ◽  
◽  
Shahroz Ali ◽  
Shahid Ur Rehman ◽  
Aqsa Shah
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Sufficient Conditions ◽  
Membership Functions ◽  
Similarity Relations ◽  
Complete Bipartite Graphs ◽  
Essential Set ◽  
Essential Sets ◽  
Necessary And Sufficient ◽  
Clustering Criterion

<abstract><p>In this paper, we investigate the theory of rough set to study graphs using the concept of orbits. Rough sets are based on a clustering criterion and we use the idea of similarity of vertices under automorphism as a criterion. We introduce indiscernibility relation in terms of orbits and prove necessary and sufficient conditions under which the indiscernibility partitions remain the same when associated with different attribute sets. We show that automorphisms of the graph $ \mathcal{G} $ preserve the indiscernibility partitions. Further, we prove that for any graph $ \mathcal{G} $ with $ k $ orbits, any reduct $ \mathcal{R} $ consists of one element from $ k-1 $ orbits of the graph. We also study the rough membership functions for paths, cycles, complete and complete bipartite graphs. Moreover, we introduce essential sets and discernibility matrices induced by orbits of graphs and study their relationship. We also prove that every essential set consists of union of any two orbits of the graph.</p></abstract>

scholarly journals Exclusive and essential sets of implicates of Boolean functions

2010 ◽  
Vol 158 (2) ◽  
pp. 81-96 ◽  
Author(s):  
Endre Boros ◽  
Ondřej Čepek ◽  
Alexander Kogan ◽  
Petr Kučera
Keyword(s):  
Boolean Functions ◽  
Essential Sets
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