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Discrete polymatroids.

Vlădoiu, Marius (2006)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Distinct equilateral triangle dissections of convex regions

Diane M. Donovan, James G. Lefevre, Thomas A. McCourt, Nicholas J. Cavenagh (2012)

Commentationes Mathematicae Universitatis Carolinae

We define a proper triangulation to be a dissection of an integer sided equilateral triangle into smaller, integer sided equilateral triangles such that no point is the vertex of more than three of the smaller triangles. In this paper we establish necessary and sufficient conditions for a proper triangulation of a convex region to exist. Moreover we establish precisely when at least two such equilateral triangle dissections exist. We also provide necessary and sufficient conditions for some convex...

Divisible designs admitting a Suzuki group as an automorphism group

Ralph-Hardo Schulz, Antonino~Giorgio Spera (1998)

Bollettino dell'Unione Matematica Italiana

Si costruiscono, facendo uso delle rette dei piani di Lüneburg e degli ovali di Tits, due classi di disegni divisibili ipersemplici che ammettono il gruppo di Suzuki S q ( q = 2 2 t + 1 con t 1 ) come gruppo di automorfismi. Inoltre si studiano le strutture ottenute determinandone le orbite di S q .

Doubly stochastic matrices and the Bruhat order

Richard A. Brualdi, Geir Dahl, Eliseu Fritscher (2016)

Czechoslovak Mathematical Journal

The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order n which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class Ω n of doubly stochastic matrices (convex hull of n × n permutation matrices). An alternative description of this partial order is given. We define a class of special faces of Ω n induced by permutation matrices,...

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