*Let be a sequence of integers (not necessarily distinct). Then there exists a subsequence of the sum of whose elements is divisible by . *

This is one of the first problems I saw when learning the… 658 more words

*Let be a sequence of integers (not necessarily distinct). Then there exists a subsequence of the sum of whose elements is divisible by . *

This is one of the first problems I saw when learning the… 658 more words

In the post Balls in Bins I wrote about a combinatorial function which denotes the minimum value of the product among all distributions of balls (so ) in bins with the constraints . 728 more words

Over the past 30-40 years, the so-called polynomial method has developed into a powerful tool in combinatorics and (additive) number theory. There has been a lot of recent interest in it after Dvir’s … 685 more words

My joint paper with Aditya Potukuchi, Pete L. Clark and John R. Schmitt is now up on arXiv: arXiv:1508.06020.

This work started a few months back when I emailed Pete and John, pointing out an easy generalization of Chevalley-Warning theorem using something known as the… 244 more words

The classical Chevalley-Warning theorem gives us a sufficient condition for a system of polynomial equations over a finite field to have common solutions. Affine blocking sets… 668 more words

When I was learning combinatorics for the first time (I was probably 16) there was this problem about distributing balls in bins (or urns) that I came across. 535 more words

The original Kakeya needle problem is to *find the least amount of area required to continuously rotate a unit line segment in the (Euclidean) plane by a full rotation…* 978 more words