With a view toward fracton theory in condensed matter, we introduce higher-moment polynomial degree-p global symmetry, acting on complex scalar/vector/tensor fields (e.g., ordinary or vector symmetry for p$=0$ and p$=1$ respectively). We relate this of $n$-dimensional space, to lower degree (either higher-moment, e.g., degree-(p-$\ell$)) subdimensional subsystem layers $(n-\ell)$-submanifolds. ...

Abstract In this paper, we study, for a given arithmetic function f , the sequence of polynomials $$(P_{n}^{f}(t))_{n=0}^{\infty }$$ ( P n f t ) = 0 <m...