22,909 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
Pattern classes and priority queues
When a set of permutations comprising a pattern class C is submitted as input
to a priority queue the resulting output is again a pattern class C'. The basis
of C' is determined for pattern classes C whose basis elements have length 3,
and is finite in these cases. An example is given of a class C with basis 2431
for which C is not finitely based
Pattern avoidance classes and subpermutations
Pattern avoidance classes of permutations that cannot be expressed as unions
of proper subclasses can be described as the set of subpermutations of a single
bijection. In the case that this bijection is a permutation of the natural
numbers a structure theorem is given. The structure theorem shows that the
class is almost closed under direct sums or has a rational generating function.Comment: 18 pages, 4 figures (all in-line
The EMC of satellite power systems and DoD C-E systems
The solar power satellite (SPS) technical parameters that are needed to accurately assess the electromagnetic compatibility (EMC) between SPS systems and DoD communications-electronics (C-E) systems are identified and assessed. The type of electromagnetic interactions that could degrade the performance of C-E systems are described and the major military installations in the southwestern portions of CONUS where specially sensitive C-E systems are being used for combat training and evaluation are identified. Classes of C-E systems that are generally in the vicinity of these military installations are considered. The Technical parameters that govern the degree of compatibility of the SPS with these C-E systems, and some technical requirements that are necessary to ensure short-term and long-term EMC are identified
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
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
Isomorphisms between pattern classes
Isomorphisms p between pattern classes A and B are considered. It is shown
that, if p is not a symmetry of the entire set of permutations, then, to within
symmetry, A is a subset of one a small set of pattern classes whose structure,
including their enumeration, is determined.Comment: 11 page
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