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40,937
Induction by Enumeration
, 2000
"... Induction by enumeration has a clear interpretation within the numerical paradigm of inductive discovery (i.e., the one pioneered by [Gold, 1967]). The concept is less easily interpreted within the firstorder paradigm discussed by [Kelly, 1996, Martin & Osherson, 1998], in which the scientist&a ..."
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Induction by enumeration has a clear interpretation within the numerical paradigm of inductive discovery (i.e., the one pioneered by [Gold, 1967]). The concept is less easily interpreted within the firstorder paradigm discussed by [Kelly, 1996, Martin & Osherson, 1998], in which the scientist
Enumeration of Lozenge Tilings of Hexagons with a Central Triangular Hole
"... . We deal with the unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a; b + m; c; a + m; b; c + m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (\Gamma1)enume ..."
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Cited by 30 (11 self)
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. We deal with the unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a; b + m; c; a + m; b; c + m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (\Gamma1
On the Enumeration of Inscribable Graphs
 Manuscript, NEC Research Institute
, 1991
"... We explore the question of counting, and estimating the number and the fraction of, inscribable graphs. In particular we will concern ourselves with the number of inscribable and circumscribable maximal planar graphs (synonym: simplicial polyhedra) on V vertices, or, dually, the number of circumscr ..."
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Cited by 22 (4 self)
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We explore the question of counting, and estimating the number and the fraction of, inscribable graphs. In particular we will concern ourselves with the number of inscribable and circumscribable maximal planar graphs (synonym: simplicial polyhedra) on V vertices, or, dually, the number of circumscribable and inscribable trivalent (synonyms: 3regular, simple) polyhedra. For small V we provide computergenerated tables. Asymptotically for large V we will prove bounds showing that these graphs are exponentially numerous, but, viewed as a fraction of all maximal planar graphs, they are exponentially rare. Many of our results are based on a lemma, the "strong 01 law for maximal planar graphs," of independent interest. This is part of a series of TMs exploring graphtheoretic consequences of the recent RivinSmith characterization of "inscribable graphs." (A graph is a set of "vertices," some pairs of which are joined by "edges." A graph is "inscribable" if it is the 1skeleton of a conve...
Enumerating Permutations by their Run Structure
"... Abstract. Motivated by a problem in quantum field theory, we study the up and down structure of circular and linear permutations. In particular, we count the length of the (alternating) runs of permutations by representing them as monomials and find that they can always be decomposed into socalled ..."
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called ‘atomic ’ permutations introduced in this work. This decomposition allows us to enumerate the (circular) permutations of a subset of N by the length of their runs. Furthermore, we rederive, in an elementary way and using the methods developed here, a result due to Kitaev on the enumeration of valleys.
Enumerating the strings of regular languages
"... Haskell code is developed for two ways to list the strings of the language defined by a regular expression: directly by set operations and indirectly by converting to and simulating an equivalent automaton. The exercise illustrates techniques for dealing with infinite ordered domains and leads to an ..."
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to an effective standard form for nondeterministic finite automata. Lazy languages are well suited to sequence generation because of the ease with which they handle infinite sequences. The problem of enumerating the strings of a regular language was proposed by Jay Misra as a lovely case in point, simple to state
Selection by Recursively Enumerable Sets?
"... Abstract. For given sets A, B, and Z of natural numbers where the members of Z are z0, z1,... in ascending order, one says that A is selected from B by Z if A(i) = B(zi) for all i. Furthermore, say that A is selected from B if A is selected from B by some recursively enumerable set, and that A is s ..."
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Abstract. For given sets A, B, and Z of natural numbers where the members of Z are z0, z1,... in ascending order, one says that A is selected from B by Z if A(i) = B(zi) for all i. Furthermore, say that A is selected from B if A is selected from B by some recursively enumerable set, and that A
Combinatorial Polytope Enumeration
, 2009
"... We describe a provably complete algorithm for the generation of a tight, possibly exact, superset of all combinatorially distinct simple nfacet polytopes in R d, along with their graphs, fvectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d−simplex. Ou ..."
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We describe a provably complete algorithm for the generation of a tight, possibly exact, superset of all combinatorially distinct simple nfacet polytopes in R d, along with their graphs, fvectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d−simplex. Our generator has implications for several outstanding problems in polytope theory, including conjectures about the number of distinct polytopes, the edge expansion of polytopal graphs, and the dstep conjecture. 1
Universal recursively enumerable sets of strings
 Developments in Language Theory (DLT’08), Lectures Notes in Comput. Sci. 5257, SpringerVerlag, Berlin, 2008, 170–182. S. Calude 21
"... Abstract. The present work clarifies the relation between domains of universal machines and r.e. prefixfree supersets of such sets. One such characterisation can be obtained in terms of the spectrum function sW (n) mapping n to the number of all strings of length n in the set W. An r.e. prefixfree ..."
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, it is investigated to which extend this results can be transferred to plain universal machines. 1
Results 1  10
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40,937