we develop a theory of stratified $lm$-filters which generalizes the theory of stratified $l$-filters. our stratification condition explicitly depends on a suitable mapping between the lattices $l$ and $m$. if $l$ and $m$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $l$-filters. based on the stratified $lm$-filters, a general theory of lattice-v...

The closest vector problem for general lattices is NP-hard. However, we can efficiently find the closest lattice points for some special lattices, such as root lattices (An, Dn and some En). In this paper, we discuss the closest vector problem on more general lattices than root lattices.

We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-v...

• The general position number of all integer grids is determined. Only very partial results were known earlier, each them required quite some effort to obtain it. main result also implies a lower bound on the multidimensional torus graphs. gp( G ) connected graph cardinality largest set S vertices such that no three pairwise distinct from lie common geodesic. n -dimensional grid P ∞ Cartesian p...