Secant tree calculus

• Autorzy: Dominique Foata , Guo-Niu Han
• Języki publikacji: EN

Abstrakty

EN

A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.

Słowa kluczowe

EN

Tree Calculus; Partial difference equations; Binary increasing labeled trees; Secant and tangent trees; End of minimal chain; Parent of maximum leaf; Bivariate distributions; Secant numbers; Entringer distribution; Alternating permutations

Kategorie tematyczne

• 05A30: q -calculus and related topics
• 11B68: Bernoulli and Euler numbers and polynomials
• 05A15: Exact enumeration problems, generating functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 12
• Strony: 1852-1870

Daty

wydano

2014-12-01

online

2014-07-20

Twórcy

autor

Dominique Foata

• Institut Lothaire

autor

Guo-Niu Han

• Université de Strasbourg et CNRS

Bibliografia

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• [5] Dominique Foata; Guo-Niu Han, The doubloon polynomial triangle, Ramanujan J., 23(2010), 107–126 (The Andrews Festschrift). http://dx.doi.org/10.1007/s11139-009-9194-9
• [6] Dominique Foata; Guo-Niu Han, Doubloons and q-secant numbers, Münster J. of Math., 3(2010), 129–150.
• [7] Dominique Foata; Guo-Niu Han, Doubloons and new q-tangent numbers, Quarterly J. Math., 62(2011), 417–432. http://dx.doi.org/10.1093/qmath/hap043
• [8] Dominique Foata; Guo-Niu Han, Finite difference calculus for alternating permutations, J. Difference Equations and Appl., 19(2013), 1952–1966. http://dx.doi.org/10.1080/10236198.2013.794794
• [9] Dominique Foata; Guo-Niu Han, Tree Calculus for Bivariate Difference Equations, J. Difference Equations and Appl., 2014, to appear, 36 pages.
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• [12] Guo-Niu Han; Arthur Randrianarivony; Jiang Zeng, Un autre q-analogue des nombres d’Euler, The Andrews Festschrift. Seventeen Papers on Classical Number Theory and Combinatorics, D. Foata, G.-N. Han eds., Springer-Verlag, Berlin Heidelberg, 2001, pp. 139–158. Sém. Lothar. Combin., Art. B42e, 22 pp.
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Identyfikatory

DOI

10.2478/s11533-014-0429-7