5 problems

A $k$-decomposition into MSTD subsets is a partition of $I_r=\{1,2,\ldots,r\}$ into $k$ subsets, each having more pairwise sums than pairwise differences. Positive proportion conje…

Fix a constant $0<c<1/2$, and let $k_n$ be a sequence of integers satisfying … Let $[0,n]=\{0,1,\dots,n\}$, and consider subsets $S\subseteq[0,n]$ that are MSTD, meaning…

For a finite set $A\subset[1,n]$, define … Here an MSTD set is a finite set satisfying $|A+A|>|A-A|$. Central-frequency conjecture. For every fixed constant $0<\alpha<1/2$, as…

For a finite set $A$, write $A+A$ for its sumset and $A-A$ for its difference set; call $A$ an MSTD set when $|A+A|>|A-A|$. Let a $P_m$-set be a set whose sumset and difference set…

Let $f_{j_1,j_2}(A)$ denote the sumset with $j_1$ copies of $A$ added and $j_2$ copies of $A$ subtracted, and let $P_n^j$-set mean a set whose generalized sumsets contain all but t…