Polar weighted homogeneous polynomials is the class of special polynomials of real variables xi, yi, i = 1, . . . , n with zi = xi + √ −1 yi which enjoys a “ polar action”. In many aspects, their behavior looks like that of complex weighted homogeneous polynomials. We study basic properties of hypersurfaces which are defined by polar weighted homogeneous polynomials.

Bbrijczky, K., N. Sauer and X. Zhu, Inexhaustible homogeneous structures, Discrete Mathematics 115 (1993) 57-63. We discuss the notions of inexhaustible, weakly inexhaustible, age-inexhaustible and closureinexhaustible for countable homogeneous structures. Then we characterize these properties of homogeneous structures in various ways. We also exhibit several examples which show that the assump...

We show that if N and M are transitive models of ZFA such that N ⊆M , N and M have the same kernel and same set of atoms, and M |=AC, then N is a Frankel-Mostowski-Specker (FMS) submodel of M if and only if M is a generic extension of N by some almost homogeneous notion of forcing. We also develop a slightly modified notion of FMS submodels to characterize the case where M is a generic extensio...

It is well known that the Lyndon words of length n can be used to construct a basis for the n-th homogeneous component of the free Lie algebra. We develop an algorithm that uses a dynamic programming table to efficiently generate the standard bracketing for all Lyndon words of length n, thus constructing a basis for the n-th homogeneous component of the free Lie algebra. The algorithm runs in l...

Kronecker products of complex characters of the symmetric group Sn have been studied in many papers. Information on special products and on the coefficients of special constituents have been obtained but there is no efficient combinatorial algorithm in sight for computing these products. In [1], products of Sn-characters with few homogeneous components and homogeneous products of characters of ...

A homogeneous set is a non-trivial, proper subset of a graph’s vertices such that all its elements present exactly the same outer neighborhood. Given two graphs, G1(V, E1), G2(V, E2), we consider the problem of finding a sandwich graph Gs(V, ES), with E1 ⊆ ES ⊆ E2, which contains a homogeneous set, in case such a graph exists. This is called the Homogeneous Set Sandwich Problem (HSSP). We give ...