Determinants involving q-Stirling numbers

Advances in Applied Mathematics

Volumn 31, Issue 4, 2003, Pages 630-642

  Ehrenborg, Richard ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242677057     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0196-8858(03)00029-0     Document Type: Article

References (20)

1. M. Aigner, A characterization of the Bell numbers, Discrete Math. 205 (1999) 207-210.
2. J. Buhler, D. Eisenbud, R. Graham, C. Wright, Juggling drops and descents, Amer. Math. Monthly 101 (1994) 507-519.
3. J. Buhler, R. Graham, A note on the binomial drop polynomial of a poset, J. Combin. Theory Ser. A 66 (1994) 321-326.
4. L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948) 987-1000.
5. J. Cigler, Eine Charakterisierung der q-Exponentialpolynome, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 208 (1999) 143-157.
6. A. de Médicis, P. Leroux, A unified combinatorial approach for q- (and p,q-) Stirling numbers, J. Statist. Plann. Inference 34 (1993) 89-105.
7. R. Ehrenborg, The Hankel determinant of exponential polynomials, Amer. Math. Monthly 107 (2000) 557-560.
8. R. Ehrenborg, M. Readdy, Juggling and applications to q-analogues, Discrete Math. 157 (1996) 107-125.
9. A.M. Garsia, J.B. Remmel, q-Counting rook configurations and a formula of Frobenius, J. Combin. Theory Ser. A 41 (1986) 246-275.
10. J. Goldman, G.-C. Rota, On the foundations of combinatorial theory. IV. Finite vector spaces and Eulerian generating functions, Stud. Appl. Math. 49 (1970) 239-258.
11. G. Labelle, P. Leroux, E. Pergola, R. Pinzani, Stirling numbers interpolation using permutations with forbidden subsequences, Discrete Math. 246 (2002) 177-195.
12. S.C. Milne, A q-analog of restricted growth functions, Dobinski's equality, and Charlier polynomials, Trans. Amer. Math. Soc. 245 (1978) 89-118.
13. S.C. Milne, Restricted growth functions, rank row matchings of partition lattices, and q-Stirling numbers, Adv. Math. 43 (1982) 173-196.
14. C. Radoux, Calcul effectif de certains déterminants de Hankel, Bull. Soc. Math. Belg. Sér. B 31 (1979) 49-55.
15. C. Radoux, Déterminant de Hankel construit sur des polynomes liés aux nombres de dérangements, European J. Combin. 12 (1991) 327-329.
16. C. Radoux, Déterminants de Hankel et théorème de Sylvester, in: Séminaire Lotharingien de Combinatoire, Saint-Nabor, 1992, in: Publ. Inst. Rech. Math. Av., Vol. 498, Univ. Louis Pasteur, Strasbourg, 1992, pp. 115-122.
17. C. Radoux, Addition formulas for polynomials built on classical combinatorial sequences, J. Comput. Appl. Math. 115 (2000) 471-477.
18. C. Radoux, The Hankel determinant of exponential polynomials: a very short proof and a new result concerning Euler numbers, Amer. Math. Monthly 109 (2002) 277-278.
19. B.E. Sagan, A maj statistic for partitions, European J. Combin. 12 (1991) 69-79.
20. M. Wachs, D. White, p, q-Stirling numbers and set partition statistics, J. Combin. Theory Ser. A 56 (1991) 27-46.