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Content, Mireille; Lemay, Francois; Leroux, Pierre

Categories de Möbius et fonctorialites: un cadre général pour l’inversion de Möbius. (French) Zbl 0449.05004

J. Comb. Theory, Ser. A 28, 169-190 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0449.05004

Cited in 2 Reviews
Cited in 27 Documents

MSC:

05A15 Exact enumeration problems, generating functions
18A10 Graphs, diagram schemes, precategories

Keywords:

Möbius inversion; partially ordered sets; monoids; finite decomposition property; categories; Möbius categories; Möbius functions; product formulas; reduced algebras; homomorphism; reduced incidence algebra; isomorphism problem; free category; triangular categories
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Full Text: DOI

References:

[1] Cartier, P.; Foata, D., Problèmes combinatoires de commutation et réarrangements, (Lecture Notes in Mathematics, No. 85 (1969), Springer-Verlag: Springer-Verlag New York/Berlin) · Zbl 0186.30101
[2] Cashwell, E. D.; Everett, C. J., The ring of number theoretic functions, Pacific J. Math., 9, 975-985 (1959) · Zbl 0092.04602
[3] Content, M., Les catégories de Möbius, (Mémoire de maîtrise (1977), Université du Québec à Montréal)
[4] P. Doubilet et G.-C. Rota; P. Doubilet et G.-C. Rota
[5] Doubilet, P.; Rota, G.-C; Stanley, R. P., The idea of generating function, (Rota, G.-C, Finite Operator Calculus (1975), Academic Press: Academic Press New York), 83-134
[6] Kelley, J. L., General Topology, ((1955), Van Nostrand: Van Nostrand Princeton, N.J), 65-66, Chap. 2 · Zbl 0066.16604
[7] Lemay, F., Catégories de Möbius, algèbres d’incidence et fonctorialités, (Mémoire de maîtrise (1978), Université du Québec à Montréal)
[8] Leroux, P., Les catégories de Möbius, Cahiers de topologie et géométrie différentielle, 16, 280-282 (1975) · Zbl 0364.18001
[9] MacLane, S., Categories for the Working Mathematician (1971), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0232.18001
[10] MacMahon, P. A., (Combinatorial Analysis, Vol. I (1915), Cambridge Univ. Press: Cambridge Univ. Press London/New York), réimpression: Chelsea, New York, 1960 · JFM 45.1271.01
[11] Mitchell, B. M., Rings with several objects, Advances in Math., 8, 1-161 (1972) · Zbl 0232.18009
[12] Nijenhuis, A.; Wilf, M. S., Combinatorial Algorithms (1975), Academic Press: Academic Press New York · Zbl 0343.68004
[13] Rota, G.-C, On the foundations of combinatorial theory, I: Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 2, 340-368 (1964), Heft 4 · Zbl 0121.02406
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