Geodesic
Planar flows and quadratic relations over semirings
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 3, pp. 441-474.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Adapting Lindström's well-known construction, we consider a wide class of functions which are generated by flows in a planar acyclic directed graph whose vertices (or edges) take weights in an arbitrary commutative semiring. We give a combinatorial description for the set of "universal" quadratic relations valid for such functions. Their specializations to particular semirings involve plenty of known quadratic relations for minors of matrices (e.g., Plücker relations) and the tropical counterparts of such relations. Also some applications and related topics are discussed.
Keywords: plücker relation, dodgson condensation, tropicalization, semiring, planar graph, network flow, lindström's lemma, Schur function, Laurent phenomenon 
@article{JAC_2012__36_3_a1,
     author = {Danilov, Vladimir I. and Karzanov, Alexander V. and Koshevoy, Gleb A.},
     title = {Planar flows and quadratic relations over semirings},
     journal = {Journal of Algebraic Combinatorics},
     pages = {441--474},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a1/}
}
TY  - JOUR
AU  - Danilov, Vladimir I.
AU  - Karzanov, Alexander V.
AU  - Koshevoy, Gleb A.
TI  - Planar flows and quadratic relations over semirings
JO  - Journal of Algebraic Combinatorics
PY  - 2012
SP  - 441
EP  - 474
VL  - 36
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a1/
LA  - en
ID  - JAC_2012__36_3_a1
ER  - 
%0 Journal Article
%A Danilov, Vladimir I.
%A Karzanov, Alexander V.
%A Koshevoy, Gleb A.
%T Planar flows and quadratic relations over semirings
%J Journal of Algebraic Combinatorics
%D 2012
%P 441-474
%V 36
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a1/
%G en
%F JAC_2012__36_3_a1
Danilov, Vladimir I.; Karzanov, Alexander V.; Koshevoy, Gleb A. Planar flows and quadratic relations over semirings. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 3, pp. 441-474. http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a1/