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arXiv · 1304.2563

Automorphisms of necklaces and sandpile groups

S. Duzhin·D. Pasechnik
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Abstract

We introduce a group naturally acting on aperiodic necklaces of length $n$ with two colours using the 1--1 correspondences between aperiodic necklaces and irreducible polynomials over the field $\F_2$ of two elements. We notice that this group is isomorphic to the quotient group of non-degenerate 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.

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S. Duzhin, D. Pasechnik. 2013-04-09. Automorphisms of necklaces and sandpile groups. https://arxiv.org/abs/1304.2563

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