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Displaying 1001 – 1020 of 2522

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Isocanted alcoved polytopes

María Jesús de la Puente, Pedro Luis Clavería (2020)

Applications of Mathematics

Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their f -vectors and checking the validity of the following five conjectures: Bárány, unimodality, 3 d , flag and cubical lower bound (CLBC). Isocanted alcoved polytopes are centrally symmetric, almost simple cubical polytopes. They are zonotopes. We show that, for each dimension, there is a unique combinatorial type. In dimension d , an isocanted alcoved polytope has 2 d + 1 - 2 vertices, its face lattice is the lattice...

Isometric classification of Sobolev spaces on graphs

M. I. Ostrovskii (2007)

Colloquium Mathematicae

Isometric Sobolev spaces on finite graphs are characterized. The characterization implies that the following analogue of the Banach-Stone theorem is valid: if two Sobolev spaces on 3-connected graphs, with the exponent which is not an even integer, are isometric, then the corresponding graphs are isomorphic. As a corollary it is shown that for each finite group and each p which is not an even integer, there exists n ∈ ℕ and a subspace L p whose group of isometries is the direct product × ℤ₂.

Currently displaying 1001 – 1020 of 2522