PORC function
From Groupprops
Definition
A function on an infinite subset
of the natural numbers is termed a Polynomial On Residue Classes function or PORC function if there exists a natural number
and polynomials
such that if
with
and
, then
.
In other words, the function behaves like a polynomial on each of the residue classes modulo
.
PORC functions are also called quasipolynomials, though that term has many other meanings in other contexts.
Facts
- Higman's PORC conjecture: For a fixed natural number
, define
for a prime
as the number of isomorphism groups of order
. Higman conjectured that for any fixed
,
is a PORC function of
.