Complex Links and Hilbert–Samuel Multiplicities

Complex Analytic Realization of Links

We present the complex analytic and principal complex analytic realizability of a link in a 3-manifold M as a tool for understanding the complex structures on the cone C(M).

"Conjectural" links in complex networks

This paper introduces the concept of Conjectural Link for Complex Networks, in particular, social networks. Conjectural Link we understand as an implicit link, not available in the network, but supposed to be present, based on the characteristics of its topology. It is possible, for example, when in the formal description of the network some connections are skipped due to errors, deliberately h...

Multiplicities and Reduction Numbers

Let (R,m) be a Cohen–Macaulay local ring and let I be an ideal. There are at least five algebras built on I whose multiplicity data affect the reduction number r(I) of the ideal. We introduce techniques from the Rees algebra theory of modules to produce estimates for r(I), for classes of ideals of dimension one and two. Previous cases of such estimates were derived for ideals of dimension zero.

Multidiameters and Multiplicities

The k-diameter of a graph 0 is the largest pairwise minimum distance of a set of k vertices in 0, i.e., the best possible distance of a code of size k in 0. A k-diameter for some k is called a multidiameter of the graph. We study the function N (k,1, D), the largest size of a graph of degree at most1 and kdiameter D. The graphical analogues of the Gilbert bound and the Hamming bound in coding t...

Eigenfamilies, Characters and Multiplicities