Quasi-random subsets of Zn

Quasi - Random Subsets of Z

Reconstructing Subsets of Zn

In this paper we consider the problem of reconstructing a subset A ⊂ Z n , up to translation, from the collection of its subsets of size k, given up to translation (its k-deck). Results of Alon, Caro, Krasikov, and Roditty [1] show that this is possible provided k > log 2 n. Mnukhin [10] showed that every subset of Z n of size k is reconstructible from its (k − 1)-deck, provided k ≥ 4. We show ...

On Random Shuffles & Subsets

Four simple algorithms are presented for producing a random rearrangement of the values in an array X[1], X[2], ..., X[n] using a pseudorandom number generator. These range from one that is naive, inefficient, and biased to one that is elegeant, efficient, and unbiased. By taking the first k entries in X one obtains a random (ordered) subset of size k.

Infinite Subsets of Random Sets of Integers

There is an infinite subset of a Martin-Löf random set of integers that does not compute any Martin-Löf random set of integers. To prove this, we show that each real of positive effective Hausdorff dimension computes an infinite subset of a Martin-Löf random set of integers, and apply a result of Miller.

Polynomial Configurations in Subsets of Random and Pseudo-random Sets

N , which are analogous to the quantitative version of the wellknown Furstenberg-Sárközy theorem due to Balog, Pintz, Pelikán, and Szemerédi. In the dense case, Balog et al showed that there is a constant C > 0 such that for all integer k 2 any subset of the first N integers of density at least C(logN) 1 4 log log log logN contains a configuration of the form {x, x+ d} for some integer d > 0. L...