12,366 research outputs found
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
Growth rates of permutation classes: categorization up to the uncountability threshold
In the antecedent paper to this it was established that there is an algebraic
number such that while there are uncountably many growth
rates of permutation classes arbitrarily close to , there are only
countably many less than . Here we provide a complete characterization of
the growth rates less than . In particular, this classification
establishes that is the least accumulation point from above of growth
rates and that all growth rates less than or equal to are achieved by
finitely based classes. A significant part of this classification is achieved
via a reconstruction result for sum indecomposable permutations. We conclude by
refuting a suggestion of Klazar, showing that is an accumulation point
from above of growth rates of finitely based permutation classes.Comment: To appear in Israel J. Mat
Strings from Feynman Graph counting : without large N
A well-known connection between n strings winding around a circle and
permutations of n objects plays a fundamental role in the string theory of
large N two dimensional Yang Mills theory and elsewhere in topological and
physical string theories. Basic questions in the enumeration of Feynman graphs
can be expressed elegantly in terms of permutation groups. We show that these
permutation techniques for Feynman graph enumeration, along with the Burnside
counting lemma, lead to equalities between counting problems of Feynman graphs
in scalar field theories and Quantum Electrodynamics with the counting of
amplitudes in a string theory with torus or cylinder target space. This string
theory arises in the large N expansion of two dimensional Yang Mills and is
closely related to lattice gauge theory with S_n gauge group. We collect and
extend results on generating functions for Feynman graph counting, which
connect directly with the string picture. We propose that the connection
between string combinatorics and permutations has implications for QFT-string
dualities, beyond the framework of large N gauge theory.Comment: 55 pages + 10 pages Appendices, 23 figures ; version 2 - typos
correcte
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