We settle the negativity conjecture of Vasconcelos for the Chern number of an ideal in certain unmixed quotients of regular local rings by explicit calculation of the Hilbert polynomials of all ideals generated by systems of parameters. Introduction Let I be an m-primary ideal in a local ring (R,m) of dimension d. Let H(I, n) = λ(R/I) denote the Hilbert function of I where λ(M) denotes the leng...

We consider extremal graph-theoretic problems on regular structures. The problems ask to maximize a certain parameter of the structures in question under the condition that the values of some other parameter(s) are constant. This is where the term isoparametric is taken from. The graph problems we consider are edge-isoperimetric problems, and the poset problems are dealing with the notion of Ma...

We describe the structure of monoid natural-valued monotone functions on an arbitrary poset. For this we provide a presentation, characterization prime elements, and description its convex hull. also study associated ring, proving that it is normal, thus Cohen-Macaulay. determine Cohen-Macaulay type, characterize Gorenstein property, Gröbner basis defining ideal. Then apply these results to qua...

If V is a faithful module for a nite group G over a eld of characteristic p > 0, then the ring of invariants need not be Cohen-Macaulay if p divides the order of G. In this article the cohomology of G is used to study the question of Cohen-Macaulayness of the invariant ring. Let R = S(V) be the polynomial ring on which G acts. Then the main result can be stated as follow: If H r (G; R) 6 = 0 fo...