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2,423
Representations of Rigid Solids: Theory, Methods, and Systems
 ACM Computing Surveys
, 1980
"... Computerbased ystems for modehng the geometry ofrigid solid objects are becoming increasingly important inmechanical nd civil engineering, architecture, computer graphics, computer vision, and other fields that deal with spatial phenomena. At the heart of such systems are symbol structures (represe ..."
Abstract

Cited by 254 (2 self)
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are the difficulties in assessing current designs, pecifying the characteristics that future systems should exhibit, and designing systems t9 meet such specifications. This paper esolves many of these difficulties by providing a coherent view, based on sound theoretical principles, of what is presently known about he
Exponential Lower Bounds for the Pigeonhole Principle
, 1992
"... In this paper we prove an exponential lower bound on the size of boundeddepth Frege proofs for the pigeonhole principle (PHP). We also obtain an ~(log log rz)depth lower bound for any polynomialsized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact ..."
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Cited by 121 (27 self)
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In this paper we prove an exponential lower bound on the size of boundeddepth Frege proofs for the pigeonhole principle (PHP). We also obtain an ~(log log rz)depth lower bound for any polynomialsized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact
Gapping as Constituent Coordination
 Linguistics and Philosophy
, 1990
"... A number of coordinate constructions in natural languages conjoin sequences which do not appear to correspond to syntactic constituents in the traditional sense. One striking instance of the phenomenon is afforded by the "gapping " construction of English, of which the following sentence i ..."
Abstract

Cited by 116 (11 self)
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A number of coordinate constructions in natural languages conjoin sequences which do not appear to correspond to syntactic constituents in the traditional sense. One striking instance of the phenomenon is afforded by the "gapping " construction of English, of which the following sentence
A 3Dimensional Representation for Fast Rendering of Complex Scenes
 Computer Graphics
, 1980
"... ..."
NorthHolland PATTERNS IN TREES*
, 1988
"... We give a general formula for the number of occurrences of a pattern, or set of patterns, in the class of ordered (planeplanted) trees with a given number of edges. The proof is combinatorial. Many known enumerations of ordered and binary trees are special cases of this formula. 1. ..."
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We give a general formula for the number of occurrences of a pattern, or set of patterns, in the class of ordered (planeplanted) trees with a given number of edges. The proof is combinatorial. Many known enumerations of ordered and binary trees are special cases of this formula. 1.
A Blossoming Algorithm for Tree Volumes of Composite Digraphs
"... Abstract. A weighted composite digraph is obtained from some weighted digraph by replacing each vertex with a weighted digraph. In this paper, we give a beautiful combinatorial proof of the formula for forest volumes of composite digraphs obtained by KelmansPakPostnikov [7]. Moreover, a generaliz ..."
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Abstract. A weighted composite digraph is obtained from some weighted digraph by replacing each vertex with a weighted digraph. In this paper, we give a beautiful combinatorial proof of the formula for forest volumes of composite digraphs obtained by KelmansPakPostnikov [7]. Moreover, a
DOI: 10.4171/OWR/2009/23 Combinatorics and Probability
, 2009
"... Abstract. The effective application of probabilistic reasoning in the study of problems in diverse areas is one of the most exciting recent developments in Mathematics. Probabilistic methods turned out to be very powerful in Discrete Mathematics, Analysis, Number Theory and Theoretical Computer Scie ..."
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, and on applications of probabilistic ideas in the study of questions in Combinatorial Number Theory and in Combinatorial Geometry.
Combinatorial interpretation for the Markoff numbers, unpublished memo
, 2003
"... In this paper we generalize the concept of Markoff numbers with the construction of Markoff polynomials. We then present a combinatorial model based on a family of recursivelydefined graphs which we call snakes, such that the Markoff polynomials and Markoff numbers are respectively weighted and un ..."
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Cited by 2 (2 self)
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and unweighted enumerators of the perfect matchings of snakes. We have found four proofs of the central combinatorial theorem; we present two of them formally and sketch the other two. At the end we conjecture a generalization of this model. 1 Markoff Polynomials 1.1
SPECTRUM AND COMBINATORICS OF RAMANUJAN TRIANGLE COMPLEXES
"... Abstract. Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the highdimensional Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property. For this purpose we prove a Ch ..."
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Abstract. Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the highdimensional Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property. For this purpose we prove a
Results 1  10
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2,423