105,370 research outputs found
Combinatorial specification of permutation classes
This article presents a methodology that automatically derives a
combinatorial specification for the permutation class C = Av(B), given its
basis B of excluded patterns and the set of simple permutations in C, when
these sets are both finite. This is achieved considering both pattern avoidance
and pattern containment constraints in permutations.The obtained specification
yields a system of equations satisfied by the generating function of C, this
system being always positiveand algebraic. It also yields a uniform random
sampler of permutations in C. The method presentedis fully algorithmic
A decorated tree approach to random permutations in substitution-closed classes
We establish a novel bijective encoding that represents permutations as
forests of decorated (or enriched) trees. This allows us to prove local
convergence of uniform random permutations from substitution-closed classes
satisfying a criticality constraint. It also enables us to reprove and
strengthen permuton limits for these classes in a new way, that uses a
semi-local version of Aldous' skeleton decomposition for size-constrained
Galton--Watson trees.Comment: New version including referee's corrections, accepted for publication
in Electronic Journal of Probabilit
The Local Structure of Tilings and their Integer Group of Coinvariants
The local structure of a tiling is described in terms of a multiplicative
structure on its pattern classes. The groupoid associated to the tiling is
derived from this structure and its integer group of coinvariants is defined.
This group furnishes part of the -group of the groupoid -algebra for
tilings which reduce to decorations of . The group itself as well as the
image of its state is computed for substitution tilings in case the
substitution is locally invertible and primitive. This yields in particular the
set of possible gap labels predicted by -theory for Schr\"odinger operators
describing the particle motion in such a tiling.Comment: 45 pages including 9 figures, LaTe
Pattern-Avoiding Involutions: Exact and Asymptotic Enumeration
We consider the enumeration of pattern-avoiding involutions, focusing in
particular on sets defined by avoiding a single pattern of length 4. As we
demonstrate, the numerical data for these problems demonstrates some surprising
behavior. This strange behavior even provides some very unexpected data related
to the number of 1324-avoiding permutations
Wreath Products of Permutation Classes
A permutation class which is closed under pattern involvement may be
described in terms of its basis. The wreath product construction X \wr Y of two
permutation classes X and Y is also closed, and we investigate classes Y with
the property that, for any finitely based class X, the wreath product X \wr Y
is also finitely based.Comment: 14 page
A criterion for separating process calculi
We introduce a new criterion, replacement freeness, to discern the relative
expressiveness of process calculi. Intuitively, a calculus is strongly
replacement free if replacing, within an enclosing context, a process that
cannot perform any visible action by an arbitrary process never inhibits the
capability of the resulting process to perform a visible action. We prove that
there exists no compositional and interaction sensitive encoding of a not
strongly replacement free calculus into any strongly replacement free one. We
then define a weaker version of replacement freeness, by only considering
replacement of closed processes, and prove that, if we additionally require the
encoding to preserve name independence, it is not even possible to encode a non
replacement free calculus into a weakly replacement free one. As a consequence
of our encodability results, we get that many calculi equipped with priority
are not replacement free and hence are not encodable into mainstream calculi
like CCS and pi-calculus, that instead are strongly replacement free. We also
prove that variants of pi-calculus with match among names, pattern matching or
polyadic synchronization are only weakly replacement free, hence they are
separated both from process calculi with priority and from mainstream calculi.Comment: In Proceedings EXPRESS'10, arXiv:1011.601
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