277,879 research outputs found
On binomial set-theoretic complete intersections in characteristic p
Using aritmethic conditions on affine semigroups we prove that for a
simplicial toric variety of codimension 2 the property of being a set-theoretic
complete intersection on binomials in characteristic holds either for all
primes , or for no prime , or for exactly one prime
Complete Intersection Lattice Ideals
In this paper we completely characterize lattice ideals that are complete
intersections or equivalently complete intersections finitely generated
semigroups of \bz^n\oplus T with no invertible elements, where is a
finite abelian group. We also characterize the lattice ideals that are
set-theoretic complete intersections on binomials
On toric varieties which are almost set-theoretic complete intersections
We describe a class of affine toric varieties that are set-theoretically
minimally defined by codim binomial equations over fields of any
characteristic
On set systems determined by intersections
AbstractThe set systems determined by intersections are studied and a sufficient condotion for this property is given. For case of graphs a necessary and sufficient condition is established. Some connections to other results are discussed
On set systems with restricted intersections modulo p and p-ary t-designs
We consider bounds on the size of families ℱ of subsets of a v-set subject to restrictions modulo a prime p on the cardinalities of the pairwise intersections. We improve the known bound when ℱ is allowed to contain sets of different sizes, but only in a special case. We show that if the bound for uniform families ℱ holds with equality, then ℱ is the set of blocks of what we call a p-ary t-design for certain values of t. This motivates us to make a few observations about p-ary t-designs for their own sake
The number of k-intersections of an intersecting family of r-sets
The Erdos-Ko-Rado theorem tells us how large an intersecting family of r-sets
from an n-set can be, while results due to Lovasz and Tuza give bounds on the
number of singletons that can occur as pairwise intersections of sets from such
a family.
We consider a natural generalization of these problems. Given an intersecting
family of r-sets from an n-set and 1\leq k \leq r, how many k-sets can occur as
pairwise intersections of sets from the family? For k=r and k=1 this reduces to
the problems described above. We answer this question exactly for all values of
k and r, when n is sufficiently large. We also characterize the extremal
families.Comment: 10 pages, 1 figur
Intersections of multiplicative translates of 3-adic Cantor sets
Motivated by a question of Erd\H{o}s, this paper considers questions
concerning the discrete dynamical system on the 3-adic integers given by
multiplication by 2. Let the 3-adic Cantor set consist of all 3-adic integers
whose expansions use only the digits 0 and 1. The exception set is the set of
3-adic integers whose forward orbits under this action intersects the 3-adic
Cantor set infinitely many times. It has been shown that this set has Hausdorff
dimension 0. Approaches to upper bounds on the Hausdorff dimensions of these
sets leads to study of intersections of multiplicative translates of Cantor
sets by powers of 2. More generally, this paper studies the structure of finite
intersections of general multiplicative translates of the 3-adic Cantor set by
integers 1 < M_1 < M_2 < ...< M_n. These sets are describable as sets of 3-adic
integers whose 3-adic expansions have one-sided symbolic dynamics given by a
finite automaton. As a consequence, the Hausdorff dimension of such a set is
always of the form log(\beta) for an algebraic integer \beta. This paper gives
a method to determine the automaton for given data (M_1, ..., M_n).
Experimental results indicate that the Hausdorff dimension of such sets depends
in a very complicated way on the integers M_1,...,M_n.Comment: v1, 31 pages, 6 figure
- …