-matrices, discrepancy and preservers
Let and be positive integers, and let and be nonnegative integral vectors. Let be the set of all -matrices with row sum vector and column vector...
3-designs from PGL.
A Bruhat order for the class of -matrices with row sum vector and column sum vector .
A Combinatorial Lemma.
A comparison of two upper bounds on the permanent of -matrices. (Ein Vergleich zweier oberer Schranken für die Permanente von -Matrizen.)
A Conjecture Concerning The Existence Of Certain Combinatorial Designs.
A construction method for complete sets of mutually orthogonal frequency squares.
A determinant formula from random walks
One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute...
A further look into combinatorial orthogonality.
A generalization of group difference sets and the matrix equation Am = dI + ...J.
A note on indecomposability of Boolean matrices
A note on inequivalent Hadamard series.
A note on majorization transforms and Ryser’s algorithm
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 tree realizations of matrices
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 problem on matrices
A remark on isotopies of digraphs and permutation matrices
A technique for computing minors of binary Hadamard matrices and application to the growth problem.
A transvection decomposition in GL(n,2)
An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.
Affine resolvable balanced incomplete block designs: a survey.
Algebraic connectivity of graphs