Invariant d'Hermite des jacobiennes de graphes pondérés

Details Invariant d'Hermite des jacobiennes de graphes pondérés Invariant d'Hermite des jacobiennes de graphes pondérés

2005-06-30

arxiv.org/abs/math/0506616v1

L'Enseignement Math\'ematique 52, 3-4 (2006) 255-266

Mathematics

Combinatorics

9 pages

Scientific paper

To any weighted graph of first Betti number b is naturally associated a lattice of dimension b, definite in a similar way that the jacobian for a Riemann surface. This class of lattices generated by graphs is particularly interesting. We show here an upperbound of the Hermite invariant of such a lattice according to b whose order is ln b. This order is optimal : it is realized by the Hermite invariant of the jacobian of a systolicly economic graph.

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