Grobner bases, abstract tubes, and inclusion-exclusion reliabilitybounds

There is a close mathematical relationship between integer grids of a particular echelon form and coherent systems in reliability in the case of states coded as integer grid points. This paper shows that such an integer representation is the link between abstract tube theory, which gives improved inclusion-exclusion bounds, and an algebraic method, Grobner bases, based on the polynomial ideal of the failure event