We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified...

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified...

In this paper we provide new characterizing properties of TDI systems, among others the following: A system of linear inequalities is TDI if and only if there exists a test set for its dual integer linear programs where all positive coordinates are equal to 1, and correspond to a set of linearly independent columns. Cook, Lovász and Schrijver’s result on the recognition – in polynomial time – o...

We construct perfect 2-colorings of the 12-hypercube that attain our recent bound on the dimension of arbitrary correlation immune functions. We prove that such colorings with parameters (x, 12 − x, 4 + x, 8 − x) exist if x = 0, 2, 3 and do not exist if x = 1. This is a translation into English of the original paper by D. G. Fon-Der-Flaass, “Perfect colorings of the 12-cube that attain the boun...

Variable dimension algorithms are a class of algorithms for computation of fixed points. They normally start at a single point and generate a path of simplices of varying dimension until a simplex that contains an approximation of a fixed point is found. This thesis analyzes, compares, and contrasts five duality models for variable dimension fixed point algorithms, namely, primal-dual subdivide...

Golomb and Welch conjectured in 1970 that there only exist perfect Lee codes for radius t = 1 or dimension n = 1, 2. It is admitted that the existence and the construction of quasi-perfect Lee codes have to be studied since they are the best alternative to the perfect codes. In this paper we firstly highlight the relationships between subset sums, Cayley graphs, and Lee linear codes and present...

Keywords: Linear codes MDS-codes AMS Subject classiication (1985) 94B05 Summary: We give several bounds for the length, dimension or minimum distance of linear block codes whose dimension equals the minimum distance of their dual codes. Zusammenfassung: Wir geben verschiedene Schranken f ur die L ange, die Dimension und den Minimalabstand linearer Blockcodes, deren Dimension gleich dem Mini-mal...