A more sums than differences (MSTD) set is a finite subset S of the integers such that |S + S| > |S − S|. We construct a new dense family of MSTD subsets of {0, 1, 2, . . . , n − 1}. Our construction gives Θ(2n/n) MSTD sets, improving the previous best construction with Ω(2/n) MSTD sets by Miller, Orosz, and Scheinerman.

When the random intersection graph G(n,m, p) proposed by Karoński, Scheinerman, and Singer-Cohen in [8] is compared with the independent-edge G(n, p), the evolutions are different under some values of m and equivalent under others. In particular, when m = nα and α > 6, the total variation distance between the graph random variables has limit 0.

In 1971 Trotter (or Bogart and Trotter) conjectured that every finite poset on at least 3 points has a pair whose removal does not decrease the dimension by more than 1. In 1992 Brightwell and Scheinerman introduced fractional dimension of posets, and they made a similar conjecture for fractional dimension. This paper settles this latter conjecture.

BACKGROUND A caring, compassionate practitioner of the medical arts is the idealized version of what makes a good doctor. If asked to think of a painting of a doctor we most likely conjure an image of a physician sitting at a patient's bedside checking the pulse with a concerned look on his face. The reality is however that cynicism, among other negative attitudes, is becoming more prominent am...