Geodesic
The Critical Exponent: a Novel Graph Invariant
Séminaire lotharingien de combinatoire, 78B (2017)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

A surprising result of FitzGerald and Horn (1977) shows that Ao α := (aijα) is positive semidefinite (p.s.d.) for every entrywise nonnegative n x n p.s.d. matrix A = (aij) if and only if α is a positive integer or α >= n-2. Given a graph G, we consider the refined problem of characterizing the set HG of entrywise powers preserving positivity for matrices with a zero pattern encoded by G. Using algebraic and combinatorial methods, we study how the geometry of G influences the set HG. Our treatment provides new and exciting connections between combinatorics and analysis, and leads us to introduce and compute a new graph invariant called the critical exponent. 

@article{SLC_2017_78B_a61,
     author = {Dominique Guillot and Apoorva Khare and Bala Rajaratnam},
     title = {The {Critical} {Exponent:} a {Novel} {Graph} {Invariant}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a61/}
}
TY  - JOUR
AU  - Dominique Guillot
AU  - Apoorva Khare
AU  - Bala Rajaratnam
TI  - The Critical Exponent: a Novel Graph Invariant
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
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ID  - SLC_2017_78B_a61
ER  - 
%0 Journal Article
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%A Apoorva Khare
%A Bala Rajaratnam
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%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a61/
%F SLC_2017_78B_a61
Dominique Guillot; Apoorva Khare; Bala Rajaratnam. The Critical Exponent: a Novel Graph Invariant. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a61/