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A Note on a OneParameter Family of CatalanLike Numbers
"... We study a family of sequences of Catalanlike numbers based on the series reversion process. Properties of these sequences are derived, including continued fraction expansions, associated orthogonal polynomials and associated Aigner matrices, which turn out to be Riordan arrays. 1 ..."
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We study a family of sequences of Catalanlike numbers based on the series reversion process. Properties of these sequences are derived, including continued fraction expansions, associated orthogonal polynomials and associated Aigner matrices, which turn out to be Riordan arrays. 1
On a oneparameter family of Riordan arrays and the weight distribution of MDS codes
"... We use the formalism of the Riordan group to study a oneparameter family of lowertriangular matrices related to the weight distribution of maximum distance separable codes. We obtain factorization results for these matrices. We then derive alternative expressions for the weight distribution of MDS ..."
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We use the formalism of the Riordan group to study a oneparameter family of lowertriangular matrices related to the weight distribution of maximum distance separable codes. We obtain factorization results for these matrices. We then derive alternative expressions for the weight distribution
Parametric Integer Programming
 RAIRO Recherche Op'erationnelle
, 1988
"... When analysing computer programs (especially numerical programs in which arrays are used extensively), one is often confronted with integer programming problems. These problems have three peculiarities: ffl feasible points are ranked according to lexicographic order rather than the usual linear ec ..."
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Cited by 206 (22 self)
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When analysing computer programs (especially numerical programs in which arrays are used extensively), one is often confronted with integer programming problems. These problems have three peculiarities: ffl feasible points are ranked according to lexicographic order rather than the usual linear
Parametric Catalan numbers and Catalan triangles
 Linear Algebra Appl
"... Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Belltype Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan n ..."
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Cited by 3 (1 self)
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Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Belltype Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan
Maximizing Performance in a Striped Disk Array
, 1990
"... Improvements in disk speeds have not kept up with improvements in processor and memory speeds. One way to correct the resulting speed mismatch is to stripe data across many disks. In this paper, we address how to stripe data to get maximum performance from the disks. Specifically, we examine how to ..."
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Cited by 140 (10 self)
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Improvements in disk speeds have not kept up with improvements in processor and memory speeds. One way to correct the resulting speed mismatch is to stripe data across many disks. In this paper, we address how to stripe data to get maximum performance from the disks. Specifically, we examine how
The Catalan numbers
"... Abstract. Catalan numbers C(n) = 1 n+1 n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n−k � � n+k n+k n. These integers are known to satisfy simple recurrence, which may be visualised in a “Catalan ..."
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triangle”, a lowertriangular twodimensional array. It is surprising that the extension of this construction to 3 dimensions generates integers B3(n, k, l) that give a 2parameter distribution of C3(n) = 1 � � 3n 2n+1 n, which may be called oder3 FussCatalan numbers, and enumerate ternary trees
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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coil array in brain imaging. With an array of five coils doubleoblique heart images were obtained in onethird of conventional scan time. Magn Reson Med 42:952962, 1999. 1999 WileyLiss, Inc. Key words: MRI; sensitivity encoding; SENSE; fast imaging; receiver coil array Among today's many medical
An endtoend discriminative approach to machine translation
 In Proceedings of the Joint International Conference on Computational Linguistics and Association of Computational Linguistics (COLING/ACL
, 2006
"... We present a perceptronstyle discriminative approach to machine translation in which large feature sets can be exploited. Unlike discriminative reranking approaches, our system can take advantage of learned features in all stages of decoding. We first discuss several challenges to errordriven disc ..."
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Cited by 161 (3 self)
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driven discriminative approaches. In particular, we explore different ways of updating parameters given a training example. We find that making frequent but smaller updates is preferable to making fewer but larger updates. Then, we discuss an array of features and show both how they quantitatively increase BLEU score
A determinant property of Catalan numbers
 Discrete Math
"... Catalan numbers arise in a family of persymmetric arrays with determinant 1. The demonstration ..."
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Cited by 7 (0 self)
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Catalan numbers arise in a family of persymmetric arrays with determinant 1. The demonstration
PASCAL, CATALAN, AND GENERAL SEQUENCE
"... the first coiumn of matrix inverses of matrices containing certain columns of Pascal's triangle, and which also can be obtained from certain diagonals of Pascal's triangle [1], [2]. These sequences S, are also the solutions for certain ballot problems, which counting process also yields t ..."
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their convolution arrays. The convolution triangles for the sequences 5 / contain determinants with special values and occur in matrix products yielding Pascal's triangle. Surprisingly enough, we can also find determinant properties which hold for any convolution array. 1. OW THE CATALAN WUIV1BERS AMD BALLOT
Results 1  10
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