Characterizations of Lambek-Carlitz type
Schwab, Emil Daniel
Archivum Mathematicum, Tome 040 (2004), p. 295-300 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The $q$-analog of the Lambek-Carlitz type characterization of exponential series is also established.

Publié le : 2004-01-01
Classification:  11A25,  13F25,  18B99 
@article{107912,
     author = {Emil Daniel Schwab},
     title = {Characterizations of Lambek-Carlitz type},
     journal = {Archivum Mathematicum},
     volume = {040},
     year = {2004},
     pages = {295-300},
     zbl = {1122.11003},
     mrnumber = {2107025},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107912}
}

Schwab, Emil Daniel. Characterizations of Lambek-Carlitz type. Archivum Mathematicum, Tome 040 (2004) pp. 295-300. http://gdmltest.u-ga.fr/item/107912/

Carlitz L. Problem E 2268, Amer. Math. Monthly 78 (1971), 1140. (1971) | MR 1536560

Content M.; Lemay F.; Leroux P. Catégories de Möbius et fonctorialités: un cadre gènèral pour l’inversion de Möbius, J. Combin. Theory Ser. A 25 (1980), 169–190. (1980) | MR 0563554 | Zbl 0449.05004

Doubilet P.; Rota G. C.; Stanley R. On the foundations of combinatorial theory (VI): the idea of generating function, Proc. of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, 267–318. | MR 0403987 | Zbl 0267.05002

Goldman J.; Rota G. C. On the foundations of combinatorial theory IV: finite-vector spaces and Eulerian generating functions, Stud. Appl. Math. 49 (1970), 239–258. (1970) | MR 0265181 | Zbl 0216.01802

Lambek J. Arithmetical functions and distributivity, Amer. Math. Monthly 73 (1966), 969–973. (1966) | MR 0202657 | Zbl 0152.03105

Langford E. Distributivity over the Dirichlet product and complete multiplicative arithmetical functions, Amer. Math. Monthly 80 (1973), 411–414. (1973) | MR 0314789

Leroux P. Les catégories de Möbius, Cahiers Topologie Géom. Différentielle Catég. 16 (1975), 280–282. (1975)

Leroux P. Catégories triangulaires. Exemples, applications, et problèmes, Rapport de recherche, Université du Québec a Montréal (1980), 72p. (1980)

Leroux P. Reduced matrices and $q$-log-concavity properties of $q$-Stirling numbers, J. Combin. Theory Ser. A (1990), 64–84. (1990) | MR 1051779 | Zbl 0704.05003

Schwab E. D. Multiplicative and additive elements in the ring of formal power series, PU.M.A. 4 (1993), 339–346. (1993) | MR 1283983 | Zbl 0806.13010

Schwab E. D. Complete multiplicativity and complete additivity in Möbius categories, Ital. J. Pure Appl. Math. 3 (1998), 37–48. (1998) | MR 1769389 | Zbl 0955.05007

Sivaramakrishnan R. Problem E 2196, Amer. Math. Monthly 77 (1970), 772. (1970)