Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
completely multiplicative functions; Möbius categories; exponential series
completely multiplicative functions; Möbius categories; exponential series
Summary:
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.
References:
[1] Carlitz L.: Problem E 2268. Amer. Math. Monthly 78 (1971), 1140. MR 1536560
[2] 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. MR 0563554 | Zbl 0449.05004
[3] 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
[4] 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. MR 0265181 | Zbl 0216.01802
[5] Lambek J.: Arithmetical functions and distributivity. Amer. Math. Monthly 73 (1966), 969–973. MR 0202657 | Zbl 0152.03105
[6] Langford E.: Distributivity over the Dirichlet product and complete multiplicative arithmetical functions. Amer. Math. Monthly 80 (1973), 411–414. MR 0314789
[7] Leroux P.: Les catégories de Möbius. Cahiers Topologie Géom. Différentielle Catég. 16 (1975), 280–282.
[8] Leroux P.: Catégories triangulaires. Exemples, applications, et problèmes. Rapport de recherche, Université du Québec a Montréal (1980), 72p.
[9] Leroux P.: Reduced matrices and $q$-log-concavity properties of $q$-Stirling numbers. J. Combin. Theory Ser. A (1990), 64–84. MR 1051779 | Zbl 0704.05003
[10] Schwab E. D.: Multiplicative and additive elements in the ring of formal power series. PU.M.A. 4 (1993), 339–346. MR 1283983 | Zbl 0806.13010
[11] Schwab E. D.: Complete multiplicativity and complete additivity in Möbius categories. Ital. J. Pure Appl. Math. 3 (1998), 37–48. MR 1769389 | Zbl 0955.05007
[12] Sivaramakrishnan R.: Problem E 2196. Amer. Math. Monthly 77 (1970), 772.
Search
Partner of
