Gessel, I. (1986). A probabilistic method for lattice path enumeration. J. Statist. Plann. Inference 14, 49-58. Home/Search Document Not in Database Summary Related Articles Check |
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Majorization in Lattice Path Enumeration And Creating Order - Tamm (Correct)
....Catalan numbers C (s) n . Note that this describes the case in which the sequence of di#erences (u n u n 1 ) n=1,2, is periodic with period length 1. In Section II we shall derive similar identities for period length 2, hereby following a probabilistic method introduced by Gessel [45], which allows to apply Lagrange inversion. For instance, it can be shown that if u (1) and u (2) are such that u (1) 2i = u (2) 2i = s ci, u (1) 2i 1 = s ci and u (2) 2i 1 = s (c ) ci, then N(u (1) 2n) N(u (2) 2n) 2 (c 2)n 1 (c 2)n 1 2n . 1.3) ....
....GESSEL s PROBABILISTIC APPROACH We saw already that the problems under consideration can be transformed into the equivalent problem of enumerating paths in an integer lattice from the origin (0, 0) to the point (n, u n ) which never touch any of the points (i, u i ) i = 0, 1, n 1. In [45] Gessel introduced a general probabilistic method to determine the number of such paths, denoted by f n , which he studied for the case that the sequence (u i ) i=1,2. is periodic. In this case the elements of the sequence (u i ) i are on the d lines u di = 0 ci and u di 1 = 0 1 ci, ....
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I. Gessel, "A probabilistic method for lattice path enumeration", J. Statist. Plann. Inference 14, 1986, 49 -- 58.
Catalan Traffic at the Beach - Niederhausen (2002) (Correct)
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Gessel, I. (1986). A probabilistic method for lattice path enumeration. J. Statist. Plann. Inference 14, 49-58.
Catalan Traffic at the Beach - Niederhausen (2002) (Correct)
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Gessel, I. (1986). A probabilistic method for lattice path enumeration. J. Statist. Plann. Inference 14, 49-58.
Exchange Symmetries in Motzkin Path and Bargraph Models.. - van Rensburg, Rechnitzer (2002) (Correct)
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I.M. Gessel, 1986, A Probabilistic Method for Lattice Path Enumeration. J. Stat. Plan. and Infer. 14, 49--58.
Exchange Symmetries in Motzkin Path and Bargraph Models of.. - van Rensburg, 2002 (2002) (Correct)
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I.M. Gessel, 1986, A Probabilistic Method for Lattice Path Enumeration. J. Stat. Plan. and Infer. 14, 49-58.
Lattice Paths Not Touching a Given Boundary - Ulrich Tamm Address (2000) (Correct)
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Gessel, I. (1986), A probabilistic method for lattice path enumeration, J. Statist. Plann. Inference 14, 49 - 58.
Walks confined in a quadrant are not always D-finite - Bousquet-Melou, Petkovsek (Correct)
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I. M. Gessel, A probabilistic method for lattice path enumeration, J. Statist. Plann. Infererence 14 (1986) 49-58.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
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I. Gessel, "A probabilistic method for lattice path enumeration", J. Statist. Plann. Inference 14, 1986, 49 -- 58.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
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I. Gessel, \A probabilistic method for lattice path enumeration", J. Statist. Plann. Inference 14,
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
No context found.
I. Gessel, "A probabilistic method for lattice path enumeration", J. Statist. Plann. Inference 14,
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