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Counting racks of order n

Abstract:

A rack on [n] can be thought of as a set of maps (f x )x∈ [n] , where each f x is a permutation of [n] such that f (x) f y =f −1 y f x f y for all x and y. In 2013, Blackburn showed that the number of isomorphism classes of racks on [n][n] is at least 2 (1/4−o(1)) n 2 and at most 2 (c+o(1)) n 2 , where c≈1.557; in this paper we improve the upper bound to 2 (1/4+o(1)) n 2 , matching the lower bound. The proof involves considering racks as loopless, edge-coloured directed multigraphs on [n], w...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Authors


Ashford, M More by this author
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Department:
St Edmund Hall
Publisher:
Electronic Journal of Combinatorics Publisher's website
Journal:
Electronic Journal of Combinatorics Journal website
Volume:
24
Issue:
2
Pages:
Article: P2.32
Publication date:
2017-06-02
Acceptance date:
2017-05-25
ISSN:
1077-8926
Pubs id:
pubs:636614
URN:
uri:e73d15ff-c49a-463c-ad6e-2283c3f9adcf
UUID:
uuid:e73d15ff-c49a-463c-ad6e-2283c3f9adcf
Local pid:
pubs:636614

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