Four Questions on Birkhoff Polytope

2000 ◽  
Vol 4 (1) ◽  
pp. 83-90 ◽  
Author(s):  
I. Pak
Keyword(s):  
Birkhoff Polytope

The number of faces of the tridiagonal Birkhoff polytope

2009 ◽  
Vol 161 (6) ◽  
pp. 867-877 ◽  
Author(s):  
L. Costa ◽  
C. M. da Fonseca ◽  
E. A. Martins
Keyword(s):  
Birkhoff Polytope ◽  
Number Of Faces

scholarly journals Face counting on an Acyclic Birkhoff polytope

2009 ◽  
Vol 430 (4) ◽  
pp. 1216-1235 ◽  
Author(s):  
Liliana Costa ◽  
C.M. da Fonseca ◽  
Enide Andrade Martins
Keyword(s):  
Birkhoff Polytope

scholarly journals On the Vertices of the d-Dimensional Birkhoff Polytope

2013 ◽  
Vol 51 (1) ◽  
pp. 161-170 ◽  
Author(s):  
Nathan Linial ◽  
Zur Luria
Keyword(s):  
Birkhoff Polytope

scholarly journals The Independence Number of the Birkhoff Polytope Graph, and Applications to Maximally Recoverable Codes

2019 ◽  
Vol 48 (4) ◽  
pp. 1425-1435 ◽  
Author(s):  
Daniel Kane ◽  
Shachar Lovett ◽  
Sankeerth Rao
Keyword(s):  
Independence Number ◽  
Birkhoff Polytope

scholarly journals Robust Hadamard Matrices, Unistochastic Rays in Birkhoff Polytope and Equi-Entangled Bases in Composite Spaces

2018 ◽  
Vol 12 (4) ◽  
pp. 473-490 ◽  
Author(s):  
Grzegorz Rajchel ◽  
Adam Gąsiorowski ◽  
Karol Życzkowski
Keyword(s):  
Hadamard Matrices ◽  
Birkhoff Polytope

scholarly journals Ehrhart Series of Polytopes Related to Symmetric Doubly-Stochastic Matrices

10.37236/4692 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Robert Davis
Keyword(s):  
Symmetric Matrices ◽  
Stochastic Matrices ◽  
Ehrhart Theory ◽  
Doubly Stochastic ◽  
Birkhoff Polytope ◽  
Ehrhart Series ◽  
Doubly Stochastic Matrices ◽  
Rational Polytope

In Ehrhart theory, the $h^*$-vector of a rational polytope often provides insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic matrices, has a unimodal $h^*$-vector, but when even small modifications are made to the polytope, the same property can be very difficult to prove. In this paper, we examine the $h^*$-vectors of a class of polytopes containing real doubly-stochastic symmetric matrices.

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