Hyperdeterminants on semilattices

Jean-Gabriel Luque (1, 2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

We compute hyperdeterminants of hypermatrices whose indices belongs in a meet-semilattice and whose entries depend only of the greatest lower bound of the indices. One shows that an elementary expansion of such a polynomial allows to generalize a theorem of Lindström to higher-dimensional determinants. And we gave as an application generalizations of some results due to Lehmer, Li and Haukkanen.

Mots clés: Hyperdeterminants; meet semilattices; GCD-matrices; multiplicative functions

Domaines: Combinatoire [math.CO]; Algèbre commutative [math.AC]; Mathématiques générales [math.GM]

Jean-Gabriel Luque. Hyperdeterminants on semilattices. Linear and Multilinear Algebra, 2007, 56 (3), pp.333-344. ⟨hal-00085204v3⟩