86 research outputs found
Generating Permutations with Restricted Containers
We investigate a generalization of stacks that we call
-machines. We show how this viewpoint rapidly leads to functional
equations for the classes of permutations that -machines generate,
and how these systems of functional equations can frequently be solved by
either the kernel method or, much more easily, by guessing and checking.
General results about the rationality, algebraicity, and the existence of
Wilfian formulas for some classes generated by -machines are
given. We also draw attention to some relatively small permutation classes
which, although we can generate thousands of terms of their enumerations, seem
to not have D-finite generating functions
Finitely labeled generating trees and restricted permutations
Generating trees are a useful technique in the enumeration of various
combinatorial objects, particularly restricted permutations. Quite often the
generating tree for the set of permutations avoiding a set of patterns requires
infinitely many labels. Sometimes, however, this generating tree needs only
finitely many labels. We characterize the finite sets of patterns for which
this phenomenon occurs. We also present an algorithm - in fact, a special case
of an algorithm of Zeilberger - that is guaranteed to find such a generating
tree if it exists.Comment: Accepted by J. Symb. Comp.; 12 page
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