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Counting pairs of nonintersecting lattice paths with respect to weighted turns. (English) Zbl 0853.05004

The authors have found a formula involving \(q\)-binomial coefficients for counting pairs of nonintersecting lattice paths which have a prescribed number of weighted turns. The formula is a \(q\)-analogue of a variant of the formula given by G. Kreweras and Y. Poupard [Eur. J. Comb. 7, 141-149 (1988; Zbl 0647.05007)].
Reviewer: I.Strazdins (Riga)

MSC:

05A15 Exact enumeration problems, generating functions
05A30 \(q\)-calculus and related topics
05C38 Paths and cycles

Citations:

Zbl 0647.05007
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References:

[1] Andrews, G. E., Theory of Partitions (1976), Addison-Wesley: Addison-Wesley New York · Zbl 0371.10001
[2] Fürlinger, J.; Hofbauer, J., \(q\)-Catalan numbers, J. Combin. Theory Ser. A, 40, 248-264 (1985) · Zbl 0581.05006
[3] I. Gessel and G. Viennot, Binomial determinants, paths, and plane partitions, unpublished manuscript.; I. Gessel and G. Viennot, Binomial determinants, paths, and plane partitions, unpublished manuscript. · Zbl 0579.05004
[4] Krattenthaler, C., The major counting of nonintersecting lattice paths and generating functions for tableaux, Mem. Amer. Math. Soc., 115, 552 (1995) · Zbl 0830.05003
[5] Kreweras, G., Joint distributions of three descriptive parameters of bridges, (Combinatoire énumérative Proc.. Combinatoire énumérative Proc., Montreal, 1985. Combinatoire énumérative Proc.. Combinatoire énumérative Proc., Montreal, 1985, Lecture Notes in Math., Vol. 1234 (1986), Springer: Springer New York), 177-191
[6] Kreweras, G.; Poupard, Y., Subdivision des nombres des Narayana suivant deux paramètres supplémentaire, Europ. J. Combin., 7, 141-149 (1986) · Zbl 0647.05007
[7] MacMahon, P. A., (Collected Papers: Combinatorics, Vol. I (1978), MIT Press: MIT Press Cambridge, MA)
[8] Narayana, T. V., Sur les treillis formés par les partitions d’un entier, Comptes Rendus Acad. Sci. Paris Ser I, 240, 1188-1189 (1955) · Zbl 0064.12705
[9] Stembridge, J., Nonintersecting paths, Pfaffians, and plane partitions, Adv. Math., 83, 96-131 (1990) · Zbl 0790.05007
[10] Sulanke, R. A., Refinements of the Narayana numbers, Bull. Inst. Comb. App., 7, 60-66 (1993) · Zbl 0804.05004
[11] Sulanke, R. A., A symmetric variation of a distribution of Kreweras and Poupard, J. Statist. Plann. Inference, 34, 291-303 (1993) · Zbl 0771.05013
[12] Zeilberger, D., Six etudes in generating functions, Internat. J. Comput. Math., 29, 201-215 (1989) · Zbl 0689.05003
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