On crossings of hyperplanes on the n-dimensional torus

[摘要] Let S be a set of hyperplanes of the n-dimensional Euclidean space R-n. For each (r(1),...,r(n)) is an element of R-n, let [r(1),...,r(n)] = {(s(1),...,s(n)) is an element of R-n \ s(i) - r(i) is an integer for each 1 less than or equal to i less than or equal to n). For each H is an element of S, let (H) over bar = {[r(1),...,r(n)] \ (r(1),..., r(n)) is an element of H}. In this paper, we study the set boolean AND(H is an element of S) (H) over bar whenever each H is an element of S satisfies a linear equation with rational coefficients of all nonconstant terms. (C) 1997 Academic Press.

[发布日期] 1997-06-01