Báo cáo toán học: "Largest minimal percolating sets in hypercubes under 2-bootstrap percolation" pdf

... for constructing large minimal percolating sets in high dimensions. Thus, we define a type of minimal percolating set which is suited to constructing large minimal percolating sets in high dimensions. ... Suppose we have a minimal percolating set A in Q n−4 which is jagged. Then we construct a jagged minimal percolating set B of size 2|A| in Q n . We build up ou...

Ngày tải lên: 08/08/2014, 12:22

... different if the ordering cone C is not pointed. So one must be careful when applying results in [4] for efficient points in the sense of (1) (as done in [2, p. 291]). For instance, Corollary 3.11 ... intersection of On Efficient Sets in R 2 465 m halfspaces, which contains a line and is therefore not pointed, as long as m<n. For instance, consider for the special case n =2andm = 1 th...

Ngày tải lên: 06/08/2014, 05:20

... Proposition 2.5, the following result is obtained. Proposition 3.1. Let α 1 , α 2 be distinct elements in F q . Then a point P = (u : v : 1) belongs to a line joining two points of D H,α 1 ∪D H,α 2 provided ... plane coordinatized over the finite field with q elements F q , is a point-set whose secants cover P G(2, q), that is, any point of P G(2, q) belongs to a line joining two distinct poi...

Ngày tải lên: 07/08/2014, 15:23

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... of cardinality 1. In the remaining case, let X be the set in S of cardinality 1, and let E = S−{X} and X = {x}. Then E is forward and backward evolutionary and each set in E is of cardinality ... Note again that the n resulting vectors are linearly independent, and moreover that they satisfy (3). The required evolutionary ordering for the resulting basis is (S n ,S n−1 , ,S 1 ). In th...

Ngày tải lên: 07/08/2014, 06:20

... Guy, Sets of integers whose subsets have distinct sums, Ann. Discrete Math., 12(1982) 141-154. [G2] R.K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, 1981. [L] W.F. Lunnon, Integer sets ... there exists an interval I i of coordinates such that I i is adjacent to the i th coordinate and d n (i)=  j∈I i d n (j). (1) We can think of the n th coordinate as the starting point w...

Ngày tải lên: 07/08/2014, 06:22

... trivial. For the inductive step note that S n can be partitioned into two sets S n,0 and S n,1 where S n,0 contains words that begin with 0 and S n,1 contains words that begin with 1. Since no word ... a minimal word S n for each n ≥ 1. 1991 Mathematics Subject Classification: Primary 68R15; Secondary 05C35. 0 Introduction In this paper we solve a particularly interesting case of the fol...

Ngày tải lên: 07/08/2014, 06:22

... edge incident with u.Thisisachievedbyselectingapoint, p 1 , u.a.r. from the free points in the bucket corresponding to u and selecting a mate, p 2 , for p 1 u.a.r. from all the remaining free points ... cubic graph: take 3n points in n buckets labelled 1 n (with three points in each bucket) and choose u.a.r. a disjoint pairing of the 3n points. If no pair contains two points from the sa...

Ngày tải lên: 07/08/2014, 06:23