Description
Consider the set of vectors over a field having non-zero coefficients only in a fixed sparse set
and multiplication defined by convolution, or the set of integers having non-zero digits (in
some base b) in a fixed sparse set. We show the existence of an optimal (or almost-optimal,
in the latter case)'magic'multiplier constant that provides a perfect hash function which
transfers the information from the given sparse coefficients into consecutive digits. Studying
the convolution case we also obtain a result of non-degeneracy for Schur functions as
polynomials in the elementary symmetric functions in positive characteristic.