An enlarged family of packing polynomials on multidimensional lattices

HereN = {0, 1, 2, ...}, while a functionf onNm or a larger domain is apacking function if its restrictionf¦Nm is a bijection ontoN. (Packing functions generalize Cantor's [1]pairing polynomials, and yield multidimensional-array storage schemes.) We call two functionsequivalent if permuting arguments makes them equal. Alsos(x) =x1 + ... +xm when x = (x1,...,xm); and such anf is adiagonal mapping iff(x) <f(y) whenever x, y εNm ands(x) <s(y). Lew [7] composed Skolem's [14], [15] diagonal packing polynomials (essentially one for eachm) to constructc(m) inequivalent nondiagonal packing polynomials on eachNm. For eachm > 1 we now construct 2m−2 inequivalent diagonal packing polynomials. Then, extending the tree arguments of the prior work, we obtaind(m) inequivalent nondiagonal packing polynomials, whered(m)/c(m) → ∞ asm → ∞. Among these we count the polynomials of extremal degree.