New Transactions on Computers Essential Sets Available

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

10.37236/8106 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
David Anderson

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.



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


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


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






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


2022 ◽  
Vol 7 (4) ◽  
pp. 5790-5807
Author(s):  
Imran Javaid ◽  
◽  
Shahroz Ali ◽  
Shahid Ur Rehman ◽  
Aqsa Shah

<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>



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


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