Does selective enumeration improve total enumeration?
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Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple package WilfPlus , which implements this process. We also compare enumeration schemes to three other systematic enumeration techniques: generating trees, substitution decompositions, and the insertion encoding.
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Abstract Using properties of ${\cal K}$ -pairs of sets, we show that every nonzero enumeration degree a bounds a nontrivial initial segment of enumeration degrees whose nonzero elements have all the same jump as a . Some consequences of this fact are derived, that hold in the local structure of the enumeration degrees, including: There is an initial segment of enumeration degrees, whose nonzero elements are all high; there is a nonsplitting high enumeration degree; every noncappable enumeration degree is high; every nonzero low enumeration degree can be capped by degrees of any possible local jump (i.e., any jump that can be realized by enumeration degrees of the local structure); every enumeration degree that bounds a nonzero element of strictly smaller jump, is bounding; every low enumeration degree below a non low enumeration degree a can be capped below a .
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Graph-theoretical concepts and definitions molecular codes enumeration and isomeric acyclic structures enumeration of polyhex systems enumeration of carcinogenic bay regions enumeration of aza-polygexes enumeration of Kekule Valence structures enumeration of 2-factors of planar polyhexes graph-theoretical indices the ID number.
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In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
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We exhibit finite injury constructions of a high Σ02 enumeration degree incomparable with all intermediate Δ02 enumeration degrees, as also of both an upwards properly Σ02 high and a low non-cuppable Σ02 enumeration degree.We also outline how to apply the same methods to prove that, for every Σ02 enumeration degree b there exists a non-cuppable degree a such that b' ≤a' and a" ≤ b", thus showing that there exist non-cuppable Σ02 enumeration degrees at every possible level of the high/low jump hierarchy.
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Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple package WILFPLUS, which implements this process. We also compare enumeration schemes to three other systematic enumeration techniques: generating trees, substitution decompositions, and the insertion encoding.
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