Results 21 to 30 of about 795 (255)
The Generating Function of Ternary Trees and Continued Fractions [PDF]
The Electronic Journal of Combinatorics, 2006 Michael Somos conjectured a relation between Hankel determinants whose entries ${1\over 2n+1}{3n\choose n}$ count ternary trees and the number of certain plane partitions and alternating sign matrices. Tamm evaluated these determinants by showing that the generating function for these entries has a continued fraction that is a special case of Gauss's ...
Ira M. Gessel, Guoce Xin
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A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method
Advances in Mathematical Physics, 2012 We discuss how to obtain black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second-order ordinary differential equations.
H. T. Cho +4 more
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Continued Fractions and Generalizations with Many Limits: A Survey [PDF]
, 2006 There are infinite processes (matrix products, continued fractions, (r, s)-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a survey of results in
Bowman, Douglas, McLaughlin, James
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Episturmian words: a survey [PDF]
, 2007 In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters.
Justin, J. +5 more
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Continued Fractions and Generalized Patterns
European Journal of Combinatorics, 2002 In [BS] Babson and Steingrimsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Let $f_{τ;r}(n)$ be the number of $1\mn3\mn2$-avoiding permutations on $n$ letters that contain exactly $r$ occurrences of $τ$, where $τ$ a generalized pattern on $k$ letters.
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A special case of rational θs for terminating θ-expansions [PDF]
Surveys in Mathematics and its Applications, 2013 There have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [A ...
Santanu Chaktaborty
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Path generating functions and continued fractions
Journal of Combinatorial Theory, Series A, 1986 From the authors' abstract: ``This paper extends \textit{P. Flajolet}'s [Discrete Math. 32, 125--161 (1980; Zbl 0445.05014)] combinatorial theory of continued fractions by obtaining the generating function for paths between horizontal lines, with arbitrary starting and ending point and weights on the steps.
Ian P. Goulden, David M. Jackson 0001
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Математичні СтудіїIn this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions.
R. Dmytryshyn +3 more
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A Generalization of the Simple Continued Fraction Algorithm [PDF]
Mathematics of Computation, 1978 In this paper we present a generalization of the continued fraction algorithm, based on a geometric and matrix-theoretic approach. We first give a geometric representation in the plane
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Matrix interpretation of multiple orthogonality [PDF]
, 2010 In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials.We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector ...
Branquinho, Amílcar +2 more
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