scholarly journals Configurations of points and topology of real line arrangements

2018 ◽  
Vol 374 (1-2) ◽  
pp. 1-35 ◽  
Author(s):  
Benoît Guerville-Ballé ◽  
Juan Viu-Sos
Keyword(s):  
Real Line ◽  
Line Arrangements ◽  
And Topology

scholarly journals Topology and combinatorics of real line arrangements

2005 ◽  
Vol 141 (06) ◽  
pp. 1578-1588 ◽  
Author(s):  
Enrique Artal Bartolo ◽  
Jorge Carmona Ruber ◽  
José Ignacio Cogolludo Agustín ◽  
Miguel Marco Buzunáriz
Keyword(s):  
Real Line ◽  
Line Arrangements

scholarly journals Real Line Arrangements and Surfaces with Many Real Nodes

2008 ◽  
pp. 47-54 ◽  
Author(s):  
Sonja Breske ◽  
Oliver Labs ◽  
Duco van Straten
Keyword(s):  
Real Line ◽  
Line Arrangements

scholarly journals Real line arrangements with the Hirzebruch property

2018 ◽  
Vol 22 (5) ◽  
pp. 2697-2711
Author(s):  
Dmitri Panov
Keyword(s):  
Real Line ◽  
Line Arrangements

scholarly journals Entropy as a Topological Operad Derivation

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1195
Author(s):  
Tai-Danae Bradley
Keyword(s):  
Information Theory ◽  
Shannon Entropy ◽  
Real Line ◽  
General Definition ◽  
Constant Multiple ◽  
The Real ◽  
And Topology ◽  
Recent Variation

We share a small connection between information theory, algebra, and topology—namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices. We begin with a brief review of operads and their representations with topological simplices and the real line as the main example. We then give a general definition for a derivation of an operad in any category with values in an abelian bimodule over the operad. The main result is that Shannon entropy defines a derivation of the operad of topological simplices, and that for every derivation of this operad there exists a point at which it is given by a constant multiple of Shannon entropy. We show this is compatible with, and relies heavily on, a well-known characterization of entropy given by Faddeev in 1956 and a recent variation given by Leinster.

scholarly journals The height of a permutation and applications to distance between real line arrangements

2020 ◽  
Vol 44 (6) ◽  
pp. 2041-2061
Author(s):  
Meirav AMRAM ◽  
Moshe COHEN ◽  
Hao Max SUN ◽  
Mina TEICHER
Keyword(s):  
Real Line ◽  
Line Arrangements
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