Groups acting on necklaces and sandpile groups

We introduce a group naturally acting on aperiodic necklaces of length n with two colors using a one-to-one correspondence between such necklaces and irreducible polynomials of degree n over the field F2 of two elements. We notice that this group is isomorphic to the quotient group of nondegenerate circulant matrices of size n over that field modulo a natural cyclic subgroup. Our groups turn out to be isomorphic to the sandpile groups for a special sequence of directed graphs. Bibliography: 15 titles.
UDC 515.16 1. INTRODUCTION This work originated in the research of the first author related to the Drinfeld associator (6). It is well known (e.g., see (5)) that the logarithm [...]