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Now showing items 1-8 of 8

#### On a Class of Aperiodic Sum-Free Sets

(Georgia Institute of Technology, 1994-10)

We show that certain natural aperiodic sum-free sets are incomplete that is that there are infinitely many n not in S which are not a sum of two element of S.

#### New Ramsey Bounds from Cyclic Graphs of Prime Order

(Georgia Institute of Technology, 1995-09)

We present new explicit lower bounds for some Ramsey numbers.
All the graphs are cyclic, and are on a prime number of vertices. We give a
partial probabilistic analysis which suggests that the cyclic Ramsey numbers
grow ...

#### Some Conditions on Periodicity for Sum-Free Sets

(Georgia Institute of Technology, 1995-07)

Cameron has introduced a natural bijection between the set of one way in nite binary sequences and
the set of sum-free sets (of positive integers), and observed that a sum-free set is ultimately periodic only
if the ...

#### Dependent Sets of Constant Weight Binary Vectors

(Georgia Institute of Technology, 1995-07)

We determine lower bounds for the number of random binary vectors,
chosen uniformly from vectors of weight k, needed to obtain a dependent set.

#### Almost Odd Random Sum-Free Sets

(Georgia Institute of Technology, 1995-07)

We show that if S_1 is a strongly complete sum-free set of positive
integers, and if S_0 is a finite sum-free set, then with positive probability a random
sum-free set U contains S_0 and is contained in S_0\cup S_1. As ...

#### The Number of Independent Sets in a Grid Graph

(Georgia Institute of Technology, 1995-07)

#### Counting Sets of Integers, No k of Which Sum to Another

(Georgia Institute of Technology, 1995-07)

We show that for every k greater or equal than 3 the number of subsets of {1,2,...,n}
containing no solution to x_1 + x_2 + ... + x_k = y, where the x_i need not
be distinct, is at most c2^{\alpha n}, where \alpha = (k-1)/k.

#### A Curious Binomial Identity

(Georgia Institute of Technology, 2009-12-07)

In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients.