arXiv subjects

Anastasia Vasil'eva

Publications and source records attributed to Anastasia Vasil'eva.

3 recordsLinked to original sources

arXiv2014

Distance Regular Colorings of $n$-Dimensional Rectangular Grid

We study the infinite graph of $n$-dimensional rectangular grid that doesn't appear distance regular and the distance regular colorings of this graph, which are defined as the distance colorings with respect to completely regular codes. It is proved that the elements of the parameter matrix of an arbitrary distance regular coloring form two monotonic sequences. It is shown that every irreducible distance regular coloring of the $n$-dimensional rectangular grid has at most $2n+1$ colors.

math.CO↗

arXiv2014

Local distributions for eigenfunctions and for perfect colorings of q-ary hypercube

Under study are the eigenfunctions and perfect colorings of the graph of $n$-dimensional $q$-ary Hamming space. We obtain the interdependence of local distributions of an eigenfunction in two orthogonal faces. We prove also an analogous result for perfect colorings.

math.CO↗

arXiv2014

Reconstruction of Eigenfunctions of q-ary n-dimensional Hypercube

Under study are eigenfunctions of $q$-ary $n$-dimensional hypercube. Given all values of an eigenfunction in the sphere we develop methods to reconstruct the function in full or in part. First, we obtain that all values of the function in the corresponding ball are uniquely determined under some supplementary conditions. Secondly, if the radius is equal to the eigenvalue number we obtain that all values of the eigenfunction are uniquiely determined under some supplementary conditions.

math.CO↗