## Combinatorial aspects of continued fractions (1980)

Venue: | Discrete Math |

Citations: | 142 - 15 self |

### BibTeX

@ARTICLE{Flajolet80combinatorialaspects,

author = {P Flajolet},

title = {Combinatorial aspects of continued fractions},

journal = {Discrete Math},

year = {1980},

volume = {32},

pages = {125--161}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

59 |
Un code pour les graphes planaires et ses applications
- Cori
- 1975
(Show Context)
Citation Context ... is due to a a b b c a c a b a a b b b a0 a I b l) b l c0 a0 c l al b2 a I a: b3 b2 b l Fig . 1s128 Schiitzenberger [25] (see also Raney [20] for applications to Lagrange's inversion formula, or Cori =-=[6]-=- in connection with planar graph enumerations) . We consider the monoid algebra' C((X)) of formal series on the set of non-commutative variables (alphabet) X with coefficients in the field of complex ... |

39 |
The average height of planted plane trees
- BRUIJN, KNUTH, et al.
- 1972
(Show Context)
Citation Context ...ition 5 is derived as a consequence of the (periodic) continued fraction expansion for a quadratic irrationality . The expansion of the Catalan series in the context of enumeration problems arises in =-=[28, 1]-=- . By utilizing various morphisms, we can derive expressions for other generating functions . Let for instanceMn,k denote the number of paths in 9, of length n containing k level steps . The generatin... |

3 |
Analyse dâ€™algorithmes de manipulation de fichiers, Institut de Recherche en Informatique et en Automatique
- Flajolet
- 1978
(Show Context)
Citation Context ...with a combinatorial interpretation of the Stieltjes matrix and the Rogers polynomials . It extends some previous results ofTouchard [27] and independentworks ofJackson [14], Read [32] and the author =-=[9]-=- . Section 2 is devoted to direct derivations of continued fraction expansions for generating series of known combinatorial quantities . Indeed the expansions of series relative to many classical comb... |

2 |
Automata,Languages and Machines,Vol.A
- Eilenberg
- 1974
(Show Context)
Citation Context ... s +E+E -E +E -E-E+ - - - with s the empty word . We shall make use of the following classical lemma . For extensive definitions, we refer the reader to standard treatises on the subject for instance =-=[8]-=- .sLemma 1. Let E,Fbe subsets ofX* . Then (i) char(E+F)=char(E)+char(F) provided E flF= 0, (ii) char(E-F)=char(E)-char(F) provided E-F has the unique factorization property, i.e . du, u'EE Vv,v' EFuv=... |

1 |
A binomial identity arising from a sorting problem
- unknown authors
- 1964
(Show Context)
Citation Context ... according to the number of minima of even value (Theorem 4) . Finally we show as a continuation of remarks of Section 1, how to derive generating series for Carlitz's cycles of binomial coefficients =-=[2]-=- . Section 3 is devoted to the enumerative properties of convergents of continued fractions . The denominator polynomials appear in a number of enumerating series for paths and diagrammes . Their clas... |

1 |
Carlitz, q-analog of the Lagrange expansion
- unknown authors
- 1974
(Show Context)
Citation Context ...rphism 1, is defined by g(a,) = for zq' and pt(bk) = zqk all j, 0, k,1, so that g(u)= zIuIq'(u) . Applying it to the equality given by Theorem 1, yields the following result first obtained by Carlitz =-=[3]-=- : Proposition 6. The generating function of paths partitioned according to area has the expansion A(z, q) =I An,kz n g k = 2.2 . Path diagrammes and set partitions 1 z2q 1 z2q3 z 2 g s This continued... |

1 |
An Introduction to Orthogonal Polynomials (Gordon and Breach
- S
- 1978
(Show Context)
Citation Context ...of the Laplace transforms of some exponential series . The continued fraction relative to the Bell numbers is implicit . in severals142 P. Flajolet analytic works relative to the Charlier polynomials =-=[4]-=- . The continued fraction relative to the odd factorial numbers Jn is classically derived as a limiting case of the continued fraction of Gauss whichexpresses the quotient of two contiguous hypergeome... |

1 |
Une nouvelle interpretation combinatoire des nombres tangents
- Dumont
- 1976
(Show Context)
Citation Context ... . . (1-qn)` Path diagrammes are related to objects considered by J . Rosen under the name of weighted lead ballot sequences [24] . They also appear in various forms in works by Strehl [27] andDumont =-=[7]-=- . However their systematicuse in enumeration problems relative to permutations is due to Frangon and Viennot [12, 13] . Definition. .A system of path diagrammes is defined by an application pos :X-->... |

1 |
Analysis of data structures under sequences of operations (in preparation
- Flajolet, Frangon, et al.
(Show Context)
Citation Context ...convergents of the continued fractions of path of unbounded height . Comparison of the three term recurrence relations with those given above completes the proof of the theorem . Es160 P. Flajolet In =-=[10]-=-, we make explicit the inversion relations corresponding to these four classes of polynomials and use them to compute in a simple way the double generating functions of the elements of the Stieltjes m... |