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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 421, Pages 81–93
(Mi znsl5751)
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This article is cited in 2 scientific papers (total in 2 papers)
Groups acting on necklaces and sandpile groups
S. V. Duzhina, D. V. Pasechnikb a St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
b Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK
Abstract:
We introduce a group naturally acting on aperiodic necklaces of length $n$ with two colours using the 1–1 correspondences between such necklaces and irreducible polynomials of degree $n$ over the field $\mathbb F_2$ 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.
Key words and phrases:
necklace, sandpile group.
Received: 19.12.2013
Citation:
S. V. Duzhin, D. V. Pasechnik, “Groups acting on necklaces and sandpile groups”, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Zap. Nauchn. Sem. POMI, 421, POMI, St. Petersburg, 2014, 81–93; J. Math. Sci. (N. Y.), 200:6 (2014), 690–697
Linking options:
https://www.mathnet.ru/eng/znsl5751 https://www.mathnet.ru/eng/znsl/v421/p81
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Abstract page: | 196 | Full-text PDF : | 63 | References: | 25 |
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