9,258 research outputs found
Editing to a Graph of Given Degrees
We consider the Editing to a Graph of Given Degrees problem that asks for a
graph G, non-negative integers d,k and a function \delta:V(G)->{1,...,d},
whether it is possible to obtain a graph G' from G such that the degree of v is
\delta(v) for any vertex v by at most k vertex or edge deletions or edge
additions. We construct an FPT-algorithm for Editing to a Graph of Given
Degrees parameterized by d+k. We complement this result by showing that the
problem has no polynomial kernel unless NP\subseteq coNP/poly
Closed-String Tachyon Condensation and the Worldsheet Super-Higgs Effect
Alternative gauge choices for worldsheet supersymmetry can elucidate
dynamical phenomena obscured in the usual superconformal gauge. In the
particular example of the tachyonic heterotic string, we use a judicious
gauge choice to show that the process of closed-string tachyon condensation can
be understood in terms of a worldsheet super-Higgs effect. The worldsheet
gravitino assimilates the goldstino and becomes a dynamical propagating field.
Conformal, but not superconformal, invariance is maintained throughout.Comment: 4 pages; v2: typos corrected, a reference added; v3: final version,
to appear in Phys. Rev. Lett. (abstract and intro modified for a broader
audience
Code loops in dimension at most 8
Code loops are certain Moufang -loops constructed from doubly even binary
codes that play an important role in the construction of local subgroups of
sporadic groups. More precisely, code loops are central extensions of the group
of order by an elementary abelian -group in the variety of loops
such that their squaring map, commutator map and associator map are related by
combinatorial polarization and the associator map is a trilinear alternating
form.
Using existing classifications of trilinear alternating forms over the field
of elements, we enumerate code loops of dimension
(equivalently, of order ) up to isomorphism. There are
code loops of order , and of order , and of order
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