The doubloon polynomial triangle

Ramanujan Journal

Volumn 23, Issue 1, 2010, Pages 107-126

  Foata, Dominique ^a   Han, Guo Niu ^b  

^a Institut Lothaire   (France)

^b UNIVERSITÉ LOUIS PASTEUR   (France)

Author keywords

Catalan triangle; Doubloon polynomial triangle; Doubloon polynomials; Poupard triangle; Reduced tangent numbers

Indexed keywords

EID: 78649640329     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11139-009-9194-9     Document Type: Article

References (16)

1. Callan, D.: A reference given in On-Line Encyclopedia of Integer Sequences for the sequence A009766.
2. Carlitz, L.: q-Bernoulli and Eulerian numbers. Trans. Am. Math. Soc. 76, 332-350 (1954).
3. Carlitz, L.: A combinatorial property of q-Eulerian numbers. Am. Math. Mon. 82, 51-54 (1975).
4. Deutsch, E.: A reference given in On-Line Encyclopedia of Integer Sequences for the sequence A009766.
5. Foata, D., Han, G.-N.: Word straightening and q-Eulerian calculus. In: Ismail, M. E. H., Stanton, D. W. (eds.) Contemporary Mathematics. q-Series from a Contemporary Perspective, vol. 254, pp. 141-156. AMS, Providence (2000).
6. Foata, D., Han, G.-N.: Doubloons and new q-tangent numbers. Preprint, 17 p. (2008).
7. Foata, D., Schützenberger, M.-P.: Nombres d'Euler et permutations alternantes. Manuscript (unabridged version), 71 p., University of Florida, Gainesville (1971). http://igd. univ-lyon1. fr/~slc/books/index. html.
8. Foata, D., Schützenberger, M.-P.: Nombres d'Euler et permutations alternantes. In: Srivastava, J. N., et al. (eds.) A Survey of Combinatorial Theory, pp. 173-187. North-Holland, Amsterdam (1973).
9. Foata, D., Strehl, V.: Euler numbers and variations of permutations. In: Colloquio Internazionale sulle Teorie Combinatorie, 1973, Tome I. Atti dei Convegni Lincei, vol. 17, pp. 119-131. Accademia Nazionale dei Lincei, Rome (1976).
10. Foata, D., Schützenberger, M.-P.: Major index and inversion number of permutations. Math. Nachr. 83, 143-159 (1978).
11. Graham, R., Zang, N.: Enumerating split-pair arrangements. J. Comb. Theory, Ser. A 115, 293-303 (2008).
12. Han, G.-N.: Calcul Denertien. Thèse de Doctorat, Publ. l'I. R. M. A., Strasbourg, 476/TS-29 (1991), 119 p. http://www-irma. u-strasbg. fr/~guoniu/papers/p05these. pdf.
13. Han, G.-N.: Une courte démonstration d'un résultat sur la Z-statistique. C. R. Acad. Sci. Paris Sér. I 314, 969-971 (1992).
14. Han, G.-N.: Une transformation fondamentale sur les réarrangements de mots. Adv. Math. 105(1), 26-41 (1994).
15. Poupard, C.: Deux propriétés des arbres binaires ordonnés stricts. Eur. J. Comb. 10, 369-374 (1989).
16. Sloane, N. J. A.: On-line Encyclopedia of Integer Sequences.