메뉴 건너뛰기




Volumn 270, Issue 1-3, 2003, Pages 177-191

Cumulants, lattice paths, and orthogonal polynomials

Author keywords

ukasiewicz paths; Continued fractions; Cumulants; Hankel determinants; Lattice path combinatorics; Motzkin paths; Orthogonal polynomials

Indexed keywords

COMPUTATIONAL METHODS; GRAPH THEORY; MATRIX ALGEBRA; THEOREM PROVING;

EID: 0041529820     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(02)00834-8     Document Type: Article
Times cited : (14)

References (35)
  • 3
  • 4
    • 0000683126 scopus 로고    scopus 로고
    • Convolution and limit theorems for conditionally free random variables
    • Bożejko M., Leinert M., Speicher R. Convolution and limit theorems for conditionally free random variables. Pacific J. Math. 175:1996;357-388.
    • (1996) Pacific J. Math. , vol.175 , pp. 357-388
    • Bozejko, M.1    Leinert, M.2    Speicher, R.3
  • 6
    • 0040313677 scopus 로고
    • Orthogonal polynomials with a constant recursion formula and an application to harmonic analysis
    • Cohen J.M., Trenholme A.R. Orthogonal polynomials with a constant recursion formula and an application to harmonic analysis. J. Funct. Anal. 59:1984;175-184.
    • (1984) J. Funct. Anal. , vol.59 , pp. 175-184
    • Cohen, J.M.1    Trenholme, A.R.2
  • 8
    • 0043287232 scopus 로고
    • Words and trees
    • M. Lothaire (Ed.), Addison-Wesley, Reading, MA
    • R. Cori, Words and trees, in: M. Lothaire (Ed.), Combinatorics on Words, Encyclopedia of Mathematics, Vol. 17, Addison-Wesley, Reading, MA, 1983, pp. 213-227.
    • (1983) Combinatorics on Words, Encyclopedia of Mathematics , vol.17 , pp. 213-227
    • Cori, R.1
  • 9
    • 0042309538 scopus 로고
    • Combinatorial aspects of continued fractions
    • Flajolet P. Combinatorial aspects of continued fractions. Discrete Math. 32:1980;125-161.
    • (1980) Discrete Math. , vol.32 , pp. 125-161
    • Flajolet, P.1
  • 10
    • 0034266828 scopus 로고    scopus 로고
    • The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions
    • Flajolet P., Guillemin F. The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions. Adv. Appl. Probab. 32:2000;750-778.
    • (2000) Adv. Appl. Probab. , vol.32 , pp. 750-778
    • Flajolet, P.1    Guillemin, F.2
  • 11
    • 0041154268 scopus 로고
    • Continued fraction methods for random walks on N and on trees, Probability measures on groups, VII
    • (Oberwolfach, 1983), Springer, Berlin
    • P. Gerl, Continued fraction methods for random walks on N and on trees, Probability measures on groups, VII (Oberwolfach, 1983), Lecture Notes in Mathematics, Vol. 1064, Springer, Berlin, 1984, pp. 131-146.
    • (1984) Lecture Notes in Mathematics , vol.1064 , pp. 131-146
    • Gerl, P.1
  • 13
    • 0009289523 scopus 로고    scopus 로고
    • On Voiculescu's R- and S-transforms for free non-commuting random variables
    • (Waterloo, ON, 1995), American Mathematical Society, Providence, RI
    • U. Haagerup, On Voiculescu's R- and S-transforms for Free Non-commuting Random Variables, Free Probability Theory (Waterloo, ON, 1995), American Mathematical Society, Providence, RI, 1997, pp. 127-148.
    • (1997) Free Probability Theory , pp. 127-148
    • Haagerup, U.1
  • 15
  • 16
    • 0042284999 scopus 로고    scopus 로고
    • Motzkin paths and powers of continued fractions
    • Art. B44e
    • A. Lascoux, Motzkin paths and powers of continued fractions, Sém. Lothar. Combin. 44 (2000) 4, Art. B44e.
    • (2000) Sém. Lothar. Combin. , vol.44 , pp. 4
    • Lascoux, A.1
  • 17
    • 0043287231 scopus 로고    scopus 로고
    • in preparation, http://www.arxiv.org/math.CO/0210443, http://www.arxiv.org/math.CO/0210444
    • F. Lehner, Cumulants in noncommutative probability. I-III, in preparation, http://www.arxiv.org/math.CO/0210442, http://www.arxiv.org/math.CO/0210443, http://www.arxiv.org/math.CO/0210444.
    • Cumulants in Noncommutative Probability. I-III
    • Lehner, F.1
  • 18
    • 33845907500 scopus 로고
    • On the vector representations of induced matroids
    • Lindström B. On the vector representations of induced matroids. Bull. London Math. Soc. 5:1973;85-90.
    • (1973) Bull. London Math. Soc. , vol.5 , pp. 85-90
    • Lindström, B.1
  • 19
    • 21844510141 scopus 로고
    • A one-parameter family of transforms, linearizing convolution laws for probability distributions
    • Nica A. A one-parameter family of transforms, linearizing convolution laws for probability distributions. Comm. Math. Phys. 168:1995;187-207.
    • (1995) Comm. Math. Phys. , vol.168 , pp. 187-207
    • Nica, A.1
  • 20
    • 0013536690 scopus 로고    scopus 로고
    • Crossings and embracings of set-partitions and q -analogues of the logarithm of the Fourier transform
    • Nica A. Crossings and embracings of set-partitions and. q -analogues of the logarithm of the Fourier transform Discrete Math. 157:1996;285-309.
    • (1996) Discrete Math. , vol.157 , pp. 285-309
    • Nica, A.1
  • 21
    • 0030079324 scopus 로고    scopus 로고
    • R-transforms of free joint distributions and non-crossing partitions
    • Nica A. R-transforms of free joint distributions and non-crossing partitions J. Funct. Anal. 135:1996;271-296.
    • (1996) J. Funct. Anal. , vol.135 , pp. 271-296
    • Nica, A.1
  • 22
    • 0041783998 scopus 로고
    • Dimension of null spaces with applications to group rings
    • Promislow D. Dimension of null spaces with applications to group rings. Canad. J. Math. 30:1978;289-300.
    • (1978) Canad. J. Math. , vol.30 , pp. 289-300
    • Promislow, D.1
  • 23
    • 0001839717 scopus 로고
    • Functional composition patterns and power series reversion
    • Raney G.N. Functional composition patterns and power series reversion. Trans. Amer. Math. Soc. 94:1960;441-451.
    • (1960) Trans. Amer. Math. Soc. , vol.94 , pp. 441-451
    • Raney, G.N.1
  • 24
    • 0038902037 scopus 로고
    • Multiplicative functions on the lattice of noncrossing partitions and free convolution
    • Speicher R. Multiplicative functions on the lattice of noncrossing partitions and free convolution. Math. Ann. 298:1994;611-628.
    • (1994) Math. Ann. , vol.298 , pp. 611-628
    • Speicher, R.1
  • 25
    • 0000003118 scopus 로고    scopus 로고
    • Boolean convolution
    • (Waterloo, ON, 1995), American Mathematical Society, Providence, RI
    • R. Speicher, R. Woroudi, Boolean Convolution, Free Probability Theory (Waterloo, ON, 1995), American Mathematical Society, Providence, RI, 1997, pp. 267-279.
    • (1997) Free Probability Theory , pp. 267-279
    • Speicher, R.1    Woroudi, R.2
  • 26
    • 0042786094 scopus 로고
    • A Green's function for nonhomogeneous random walks on free products
    • Trenholme A.R. A Green's function for nonhomogeneous random walks on free products. Math. Z. 199:1988;425-441.
    • (1988) Math. Z. , vol.199 , pp. 425-441
    • Trenholme, A.R.1
  • 28
    • 0042284993 scopus 로고
    • A combinatorial theory for general orthogonal polynomials with extensions and applications, orthogonal polynomials and applications
    • (Bar-le-Duc, 1984), Springer, Berlin
    • G. Viennot, A Combinatorial Theory for General Orthogonal Polynomials with Extensions and Applications, Orthogonal Polynomials and Applications (Bar-le-Duc, 1984), Lecture Notes in Mathematics, Vol. 1171, Springer, Berlin, 1985, pp. 139-157.
    • (1985) Lecture Notes in Mathematics , vol.1171 , pp. 139-157
    • Viennot, G.1
  • 29
    • 0001146474 scopus 로고
    • Symmetries of some reduced free product C*-algebras, operator algebras and their connections with topology and ergodic theory
    • (Buşteni, 1983), Springer, Berlin
    • D. Voiculescu, Symmetries of Some Reduced Free Product C*-Algebras, Operator Algebras and Their Connections with Topology and Ergodic Theory (Buşteni, 1983), Lecture Notes in Mathematics, Vol. 1132, Springer, Berlin, 1985, pp. 556-588.
    • (1985) Lecture Notes in Mathematics , vol.1132 , pp. 556-588
    • Voiculescu, D.1
  • 30
    • 0000404789 scopus 로고
    • Addition of certain noncommuting random variables
    • Voiculescu D. Addition of certain noncommuting random variables. J. Funct. Anal. 66:1986;323-346.
    • (1986) J. Funct. Anal. , vol.66 , pp. 323-346
    • Voiculescu, D.1
  • 31
    • 0003251321 scopus 로고    scopus 로고
    • Lectures on Probability Theory and Statistics (Saint-Flour, 1998), Lecture Notes in Mathematics, Springer, Berlin
    • D. Voiculescu, Lectures on Free Probability Theory, Lectures on Probability Theory and Statistics (Saint-Flour, 1998), Lecture Notes in Mathematics, Vol. 1738, Springer, Berlin, 2000, pp. 279-349.
    • (2000) Lectures on Free Probability Theory , vol.1738 , pp. 279-349
    • Voiculescu, D.1
  • 32
  • 33
    • 0003047501 scopus 로고
    • An approach to the theory of pressure broadening of spectral lines, probability and information theory, II
    • Springer, Berlin
    • W. von Waldenfels, An Approach to the Theory of Pressure Broadening of Spectral Lines, Probability and Information Theory, II, Lecture Notes in Mathematics, Vol. 296, Springer, Berlin, 1973, pp. 19-69.
    • (1973) Lecture Notes in Mathematics , vol.296 , pp. 19-69
    • Von Waldenfels, W.1
  • 34
    • 0010066694 scopus 로고
    • Interval partitions and pair interactions, séminaire de probabilités, IX
    • (Seconde Partie, Univ. Strasbourg, Strasbourg, années universitaires 1973/1974 et 1974/1975) Springer, Berlin
    • W. von Waldenfels, Interval Partitions and Pair Interactions, Séminaire de Probabilités, IX (Seconde Partie, Univ. Strasbourg, Strasbourg, années universitaires 1973/1974 et 1974/1975), Lecture Notes in Mathematics, Vol. 465, Springer, Berlin, 1975, pp. 565-588.
    • (1975) Lecture Notes in Mathematics , vol.465 , pp. 565-588
    • Von Waldenfels, W.1
  • 35
    • 0042284994 scopus 로고    scopus 로고
    • On the powers of Motzkin paths
    • Art. B44f
    • J. Zeng, On the powers of Motzkin paths, Sém. Lothar. Combin. 44 (2000) 2 Art. B44f.
    • (2000) Sém. Lothar. Combin. , vol.44 , pp. 2
    • Zeng, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.