2,600 research outputs found
Improved Lower Bounds on the Compatibility of Multi-State Characters
We study a long standing conjecture on the necessary and sufficient
conditions for the compatibility of multi-state characters: There exists a
function such that, for any set of -state characters, is
compatible if and only if every subset of characters of is
compatible. We show that for every , there exists an incompatible set
of -state
characters such that every proper subset of is compatible. Thus, for every .
This improves the previous lower bound of given by Meacham (1983),
and generalizes the construction showing that given by Habib and
To (2011). We prove our result via a result on quartet compatibility that may
be of independent interest: For every integer , there exists an
incompatible set of
quartets over
labels such that every proper subset of is compatible. We contrast this
with a result on the compatibility of triplets: For every , if is
an incompatible set of more than triplets over labels, then some
proper subset of is incompatible. We show this upper bound is tight by
exhibiting, for every , a set of triplets over taxa such
that is incompatible, but every proper subset of is compatible
-adic Beilinson conjecture for ordinary Hecke motives associated to imaginary quadratic fields
The purpose of this article is to give an overview of the series of papers
[BK1], [BK2] concerning the -adic Beilinson conjecture of motives associated
to Hecke characters of an imaginary quadratic field , for a prime which
splits in
Heterotic warped Eguchi-Hanson spectra with five-branes and line bundles
We consider heterotic strings on a warped Eguchi-Hanson space with five-brane
and line bundle gauge fluxes. The heterotic string admits an exact CFT
description in terms of an asymmetrically gauged SU(2)xSL(2,R) WZW model, in a
specific double scaling limit in which the blow-up radius and the string scale
are sent to zero simultaneously. This allows us to compute the perturbative 6D
spectra for these models in two independent fashions: i) Within the
supergravity approximation we employ a representation dependent index; ii) In
the double scaling limit we determine all marginal vertex operators of the
coset CFT. To achieve agreement between the supergravity and the CFT spectra,
we conjecture that the untwisted and the twisted CFT states correspond to the
same set of hyper multiplets in supergravity. This is in a similar spirit as a
conjectured duality between asymptotically linear dilaton CFTs and little
string theory living on NS-five-branes. As the five-brane charge is
non-vanishing, heterotic (anti-)five-branes have to be added in order to cancel
irreducible gauge anomalies. The local spectra can be combined in such a way
that supersymmetry is preserved on the compact resolved T^4/Z_2 orbifold by
choosing the local gauge fluxes appropriately.Comment: 1+36 pages LaTe
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