On two conjectures about the intersection distribution

Confirming Two Conjectures About the Integer Partitions

For a given integer n, let 4n denote the set of all integer partitions *1 *2 } } } *m>0 (m 1), of n. For the dominance order ``P'' on 4n , we show that if two partitions *, + are both chosen from 4n uniformly at random, and independent of each other, then Pr(*P+) 0 as n . This statement answers affirmatively a question posed by Macdonald in 1979. The proof is based on the limit joint distributi...

On Two Conjectures of Franz Hering about Convex Surfaces

In this paper we show that from the point of view of the Baire categories for most convex bodies no shadow boundary is included in a hyperplane. A related, more quantitative question is also considered. It receives in general a negative answer and in the CLcase a positive one, but remains open in the Ct-case.

Two Conjectures on Convex Curves

Department of Mathematics, University of Oil and Gas (Gubkin) Moscow 117036, Russia [email protected] Department of Mathematics, University of Stockholm S-10691, Sweden, [email protected] Abstra t. In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP3. Namely...

Some Conjectures About Cyclotomic Integers

On Berry's conjectures about the stable order in PCF

PCF is a sequential simply typed lambda calculus language. There is a unique order-extensional fully abstract cpo-model of PCF, built up from equivalence classes of terms. In 1979, Gérard Berry defined the stable order in this model and proved that the extensional and the stable order together form a bicpo. He made the following two conjectures: 1) “Extensional and stable order form not only a ...