30,101 research outputs found
Permutation Classes of Polynomial Growth
A pattern class is a set of permutations closed under the formation of
subpermutations. Such classes can be characterised as those permutations not
involving a particular set of forbidden permutations. A simple collection of
necessary and sufficient conditions on sets of forbidden permutations which
ensure that the associated pattern class is of polynomial growth is determined.
A catalogue of all such sets of forbidden permutations having three or fewer
elements is provided together with bounds on the degrees of the associated
enumerating polynomials.Comment: 17 pages, 4 figure
Sorting with a forklift
A fork stack is a generalised stack which allows pushes and pops of several
items at a time. We consider the problem of determining which input streams can
be sorted using a single forkstack, or dually, which permutations of a fixed
input stream can be produced using a single forkstack. An algorithm is given to
solve the sorting problem and the minimal unsortable sequences are found. The
results are extended to fork stacks where there are bounds on how many items
can be pushed and popped at one time. In this context we also establish how to
enumerate the collection of sortable sequences.Comment: 24 pages, 2 figure
The enumeration of three pattern classes using monotone grid classes
The structure of the three pattern classes defined by the sets of forbidden permutations \{2143,4321\}, \{2143,4312\} and \{1324,4312\} is determined using the machinery of monotone grid classes. This allows the permutations in these classes to be described in terms of simple diagrams and regular languages and, using this, the rational generating functions which enumerate these classes are determined
Subclasses of the separable permutations
We prove that all subclasses of the separable permutations not containing
Av(231) or a symmetry of this class have rational generating functions. Our
principal tools are partial well-order, atomicity, and the theory of strongly
rational permutation classes introduced here for the first time
The enumeration of permutations avoiding 2143 and 4231
We enumerate the pattern class Av(2143, 4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes
Inflations of Geometric Grid Classes: Three Case Studies
We enumerate three specific permutation classes defined by two forbidden
patterns of length four. The techniques involve inflations of geometric grid
classes
X-ray Localization of the Globular Cluster G1 with XMM-Newton
We present an accurate X-ray position of the massive globular cluster G1 by
using XMM-Newton and the Hubble Space Telescope (HST). The X-ray emission of G1
has been detected recently with XMM-Newton. There are two possibilities for the
origin of the X-ray emission. It can be either due to accretion of the central
intermediate-mass black hole, or by ordinary low-mass X-ray binaries. The
precise location of the X-ray emission might distinguish between these two
scenarios. By refining the astrometry of the XMM-Newton and HST data, we
reduced the XMM-Newton error circle to 1.5". Despite the smaller error circle,
the precision is not sufficient to distinguish an intermediate-mass black hole
and luminous low-mass X-ray binaries. This result, however, suggests that
future Chandra observations may reveal the origin of the X-ray emission.Comment: 4 pages, 2 figures; accepted for publication in Ap
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