The calculation of crystal structure from X-ray diffraction data requires that the phases of the " structure factors " (Fourier coefficients) determined by scattering be deduced from the absolute values of those structure factors. Motivated by a question of Herbert Hauptman, we consider the problem of determining phases by direct algebraic means in the case of crystal structures with n equal at...

In Ufnarovski (1989), the concept of automaton algebras is introduced. These are quotients of the non-commutative polynomial ring where the defining ideal allows some Gröbner basis with a regular set of leading words. However, nothing is reflected concerning the whole structure of the Gröbner basis (except of course for monomial algebras). In this paper we introduce the concept of regular Gröbn...

The (semi)standard Young tableau have been known since Hodge and Littlewood to naturally index a basis for the multihomogeneous coordinate rings of flag varieties under the Plicker embedding. In representation theory, the irreducible representations of GL,(C) arise as the multihomogeneous components of these rings. I introduce a new class of straight tableau by slightly weakening the requiremen...

The (semi)standard Young tableau have been known since Hodge and Littlewood to naturally index a basis for the multihomogeneous coordinate rings of flag varieties under the Plücker embedding. In representation theory, the irreducible representations of GLn(C) arise as the multihomogeneous components of these rings. I introduce a new class of straight tableau by slightly weakening the requiremen...

This special issue on Computer algebra and computer analysis was initiated by a session with the same title at the Third International ISAAC Congress, which took place in Berlin, 2001. The guest editors K. Gatermann and W. Koepf organized this session in order to stimulate the interaction between Computer Algebra and Analysis. In this special issue we have collected articles by participants of ...

In this paper, we study the vector invariants, F[m V2] Cp , of the 2-dimensional indecomposable representation V2 of the cylic group, Cp, of order p over a field F of characteristic p. This ring of invariants was first studied by David Richman [18] who showed that this ring required a generator of degree m(p−1), thus demonstrating that the result of Noether in characteristic 0 (that the ring of...

Abstract We introduce the concept of subalgebra spectrum, Sp ( A ), for a finite codimension in $$\mathbb {K}[x]$$ K [ x ] . The spectrum is subset underlying field. also tool, characteristic polynomial , which has as its set zeroes. ca...