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A note on majorization transforms and Ryser’s algorithm

Geir Dahl (2013)

Special Matrices

The notion of a transfer (or T -transform) is central in the theory of majorization. For instance, it lies behind the characterization of majorization in terms of doubly stochastic matrices. We introduce a new type of majorization transfer called L-transforms and prove some of its properties. Moreover, we discuss how L-transforms give a new perspective on Ryser’s algorithm for constructing (0; 1)-matrices with given row and column sums.

A note on representing dowling geometries by partitions

František Matúš, Aner Ben-Efraim (2020)

Kybernetika

We prove that a rank 3 Dowling geometry of a group H is partition representable if and only if H is a Frobenius complement. This implies that Dowling group geometries are secret-sharing if and only if they are multilinearly representable.

A note on tree realizations of matrices

Alain Hertz, Sacha Varone (2007)

RAIRO - Operations Research

It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i,j,k,l.

A parallelogram configuration condition in nets

Jitka Markvartová (1993)

Archivum Mathematicum

After describing a (general and special) coordinatization of k -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in k -nets with small degree k .

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