The understanding of which Kronecker structures that are close to a given structure is revealed by the Kronecker structure hierarchy, i.e., the strati cation of the Kronecker canonical form. For a given matrix pencil A B, the Kronecker structure hierarchy shows all structures that are within the closure of orbit(A B), and each structure, whose orbit's closure contains A B. In order to gain new ...

in this paper we define ?-independent (a weak-version of independence), kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and sidon sets. these sets have the lacunarity or thinness property and are very useful indeed. for example varopoulos used the kronecker sets to prove the malliavin theorem. in t...

Stochastic Kronecker Product Graphs are an interesting and useful class of Generative Network Models. They can be fitted using a fast Maximum Likelihood Estimator and reproduce many important statistical properties commonly found in large real-world networks. However, they suffer from an unfortunate drawback: the need to pad the Stochastic Kronecker Product Graph with isolated vertices. To addr...

We show that the Kronecker coefficients indexed by two two–row shapes are given by quadratic quasipolynomial formulas whose domains are the maximal cells of a fan. Simple calculations provide explicitly the quasipolynomial formulas and a description of the associated fan. These new formulas are obtained from analogous formulas for the corresponding reduced Kronecker coefficients and a formula r...

We provide counter–examples to Mulmuley’s SH conjecture for the Kronecker coefficients. This conjecture was proposed in the setting of Geometric Complexity Theory to show that deciding whether or not a Kronecker coefficient is zero can be done in polynomial time. We also provide a short proof of the #P–hardness of computing the Kronecker coefficients. Both results rely on the connections betwee...

Prescribed Gauss-Kronecker curvature problems are widely studied in the literature. Famous among them is the Minkowski problem. It was studied by H. Minkowski, A.D. Alexandrov, H. Lewy, A.V. Pogorelov, L. Nirenberg and at last solved by S.Y. Cheng and S.T. Yau [CY]. After that, V.I.Oliker [O] researched the arbitrary hypersurface with prescribed Gauss curvature in Euclidean space. On the other ...

In the late 1930’s Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n large enough, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but only on the values of their remaining parts. We compute the exact value of n when ...

A set of integers S is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant. We transform the problem of calculating ε-Kronecker constants for finite sets of d elements into a geometric optimization problem. Using this approach we can explicitly determine the ε-Kronecker constant fo...

We provide counter–examples to Mulmuley’s strong saturation conjecture (strong SH) for the Kronecker coefficients. This conjecture was proposed in the setting of Geometric Complexity Theory to show that deciding whether or not a Kronecker coefficient is zero can be done in polynomial time. We also provide a short proof of the #P–hardness of computing the Kronecker coefficients. Both results rel...

A common assumption in the design and analysis of many MIMO transmission schemes is the so-called Kronecker model. This model is often a crucial step to obtain mathematically tractable solutions, but has also been criticized for being unrealistic. In this paper, we present a numerical approach to determine a channel whose statistics is as far from being Kronecker as possible, keeping only an as...