It is well known that if $\varphi$ is a Schwartz function on $\mathbb{R}$ (i.e. smooth and decaying at infinity faster than polynomials), then its Fourier transform decays faster than polynomials. More precisely, for any $M>0$ there exists a constant $C_M>0$ such that \begin{equation}\tag{1}\labe...

There are two great general sources for Gray codes on combinatorial objects you might enjoy: Frank Ruskey's "Combinatorial Generation" book: http://tinyurl.com/yly4pq7 Don Knuth's "Art of Computer Programming", Vol. 4, Fascicle 2-4 (published separately - all excellent), see https://www-cs-facu...