We study edge complexity, the minimum Fourier $\ell^1/\ell^2$ ratio of a graph's adjacency matrix over cyclic vertex labelings. For $K_{m,n}$, with $1\leq m\leq n$, we reduce the problem to minimizing the Fourier $\ell^1$-norm of indicators of $m$-element subsets of $\mathbb Z_{m+n}$. We prove the sharp bound $\operato...
S. Ferguson, V. Gupta, A. Iosevich et al.· 0 citations
We study the additive energy and the Fourier approximation of graph adjacency matrices labeled by a cyclic group. For a graph with $N$ vertices, $s$ edges and adjacency matrix $M$, the additive energy of its directed edge set is at most $\min\{(2s)^3,N^2\operatorname{tr}(M^4)\}$, and equality in the spectral bound hold...
V. Gupta, S. Ferguson, A. Iosevich et al.· 0 citations
Fuglede's conjecture in $\mathbb{F}_p^d$ says that a nonempty set tiles by translation if and only if it is spectral. We prove the conjecture in $\mathbb{F}_2^8$ and $\mathbb{F}_{11}^3$. Over $\mathbb{F}_2$ we show more generally that the Fourier support of a nonconstant indicator of density different from one half con...
S. Ferguson, J. Iosevich· 0 citations
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