1,494 research outputs found
A combinatorial approach to knot recognition
This is a report on our ongoing research on a combinatorial approach to knot
recognition, using coloring of knots by certain algebraic objects called
quandles. The aim of the paper is to summarize the mathematical theory of knot
coloring in a compact, accessible manner, and to show how to use it for
computational purposes. In particular, we address how to determine colorability
of a knot, and propose to use SAT solving to search for colorings. The
computational complexity of the problem, both in theory and in our
implementation, is discussed. In the last part, we explain how coloring can be
utilized in knot recognition
Strongly solvable spherical subgroups and their combinatorial invariants
A subgroup H of an algebraic group G is said to be strongly solvable if H is
contained in a Borel subgroup of G. This paper is devoted to establishing
relationships between the following three combinatorial classifications of
strongly solvable spherical subgroups in reductive complex algebraic groups:
Luna's general classification of arbitrary spherical subgroups restricted to
the strongly solvable case, Luna's 1993 classification of strongly solvable
wonderful subgroups, and the author's 2011 classification of strongly solvable
spherical subgroups. We give a detailed presentation of all the three
classifications and exhibit interrelations between the corresponding
combinatorial invariants, which enables one to pass from one of these
classifications to any other.Comment: v3: 58 pages, revised according to the referee's suggestions; v4:
numbering of sections changed to agree with the published versio
Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards
We examine the proposal made recently that the su(3) modular invariant
partition functions could be related to the geometry of the complex Fermat
curves. Although a number of coincidences and similarities emerge between them
and certain algebraic curves related to triangular billiards, their meaning
remains obscure. In an attempt to go beyond the su(3) case, we show that any
rational conformal field theory determines canonically a Riemann surface.Comment: 56 pages, 4 eps figures, LaTeX, uses eps
Maximal disk based histogram for shape retrieval
2002-2003 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe
The total coordinate ring of a wonderful variety
We study the cone of effective divisors and the total coordinate ring of
wonderful varieties, with applications to their automorphism group. We show
that the total coordinate ring of any spherical variety is obtained from that
of the associated wonderful variety by a base change of invariant subrings.Comment: Final version, to appear in Journal of Algebr
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