A combinatorial proof of Marstrand’s theorem for products of regular Cantor sets

Combinatorial proof of Muchnik's theorem

A Combinatorial Theorem on Systems of Sets

It is quite easy to see that (2) and (3) give best possible results. Upper estimates for n were also given in [2] if either (Alt..., An)eS(k, </, m) and /<^(m+l) or if (Alt..., An)eS(k, I, m) and l^^(m+k), but the results in these cases are not best possible. Other results of this kind have been established in [3] and [4] which settle certain conjectures made in [2]. In this note we establish t...

A combinatorial proof of Gotzmann's persistence theorem for monomial ideals

Gotzmann proved the persistence for minimal growth for ideals. His theorem is called Gotzmann’s persistence theorem. In this paper, based on the combinatorics on binomial coefficients, a simple combinatorial proof of Gotzmann’s persistence theorem in the special case of monomial ideals is given. Introduction Let K be an arbitrary field, R = K[x1, x2, . . . , xn] the polynomial ring with deg(xi)...

There are no C-stable intersections of regular Cantor sets

Regular interval Cantor sets of S and minimality

1 It is known that not every Cantor set of S is C-minimal. In this work we prove that every member of a subfamily of the called regular interval Cantor set is not C-minimal. We also prove in general, for a even large class of Cantor sets, that any member of such family can be C-minimal, for any 2 > 0.