5 papers
Product-free subsets of
Leonardo Franchi, W. T. Gowers, Fredy Yip
The third problem in Ben Green's collection of 100 open problems asks whether an open subset of that does not contain with must have measure at most 1/3. We…
On the sum of the largest and smallest eigenvalues of graphs with high odd girth
Fredy Yip
The sum of the maximum and minimum eigenvalues, and the odd girth of a graph both measure bipartiteness. We seek to relate these measures. In particular, for an odd i…
Multivariate and quantitative ErdÅs-Kac laws for Beatty sequences
Fredy Yip
The classical ErdÅs-Kac theorem states that for chosen uniformly at random from , the random variable converges in distri…
On a problem of ErdÅs and Ingham
Fredy Yip
We give a short and elementary argument answering a question of ErdÅs and Ingham negatively. ErdÅs and Ingham showed that a Tauberian estimate they considered was equivalent to t…
Combinatorial foundations for solvable chaotic local Euclidean quantum circuits in two dimensions
Fredy Yip
We investigate a graph-theoretic problem motivated by questions in quantum computing concerning the propagation of information in quantum circuits. A graph is said to be a boun…