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...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2014-08, Vol.200 (6), p.44
Main Authors: Duzhin, S.V, Pasechnik, D.V
Format: Article
Language:English
Subjects:
Jewelry
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Summary: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.
ISSN:1072-3374
1573-8795