Structural conditions on the support of a multivariate polynomial system are developed for which the Dixon-based resultant methods compute exact resultants. For cases when this cannot be done, an upper bound on the degree of the extraneous factor in the projection operator can be determined a priori, thus resulting in quick identification of the extraneous factor in the projection operator. (Fo...

Let C be a clutter with a perfect matching e1, . . . , eg of König type and let ∆C be the Stanley-Reisner complex of the edge ideal of C. If all c-minors of C have a free vertex and C is unmixed, we show that ∆C is pure shellable. We are able to describe in combinatorial terms when ∆C is pure. If C has no cycles of length 3 or 4, then it is shown that ∆C is pure if and only if ∆C is pure shella...

In this paper, we study the structure of cyclic, quasi cyclic, constacyclic codes and their skew codes over the finite ring R. The Gray images of cyclic, quasi cyclic, skew cyclic, skew quasi cyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The parameters of quantum error corr...

We give a new and simple proof that unmixed local rings having Hilbert-Kunz multiplicity equal to 1 must be regular.

Let A be an integral matrix whose set of column vectors is A = {v1, . . . , vq} and let A(P ) be the Ehrhart ring of P = conv(A). We are able to show that if A is the incidence matrix of a d-uniform unmixed clutter with covering number g and the system x ≥ 0;xA ≥ 1 is TDI, then the Castelnuovo-Mumford regularity of A(P ) is sharply bounded by (d − 1)(g − 1). Let R = K[x1, . . . , xn] be a polyn...

Let p be prime and Zpn a degree n unramified extension of the ring of p-adic integers Zp. In this paper we give an overview of some very fast deterministic algorithms for common operations in Zpn modulo p . Combining existing methods with recent work of Kedlaya and Umans about modular composition of polynomials, we achieve quasi-linear time algorithms in the parameters n and N , and quasi-linea...