Geodesic
Arithmetical Functions and Distributivity
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 491-496

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we shall present a result about incidence functions on a locally finite partially ordered set, a result which is related to theorems of Lambek [2] and Subbarao [6]. Our terminology and notation will be that of Smith [4, 5] and Rota [7].Let (L, ≤) be a partially ordered set which is locally finite in the sense that for all x, y ∊ L the interval [x, y] = {z | x ≤ z ≤ y} is finite. Denote by A(L, ≤) the set of functions f from L × L into some field, which is fixed once and for all, such that f(x, y) = 0 whenever x ≰ y. 
McCarthy, P. J. Arithmetical Functions and Distributivity. Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 491-496. doi: 10.4153/CMB-1970-089-8
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[1] 1. Carlitz, L., Arithmetic functions in an unusual setting, Amer. Math. Monthly 73 (1966), 582-590. Google Scholar

[2] 2. Lambek, J., Arithmetical functions and distributivity, Amer. Math. Monthly 73 (1966), 969-973. Google Scholar

[3] 3. Narkiewicz, W., On a class of arithmetical convolutions, Colloq. Math. 10 (1963), 81-94. Google Scholar

[4] 4. Smith, David, Incidence functions as generalized arithmetic functions, I, Duke Math. J. 36 (1967), 617-634. Google Scholar

[5] 5. Smith, David Incidence functions as generalized arithmetic functions, III, Duke Math. J. 36 (1969), 353-368. Google Scholar

[6] 6. Subbarao, M. V., Arithmetic functions and distributivity, Amer. Math. Monthl. 75 (1968), 984-989. Google Scholar

[7] 7. Rota, Gian-Carlo, On the foundations of combinatorial theory, I, Theory of M?bius functions, Z. Wahrsch. 2 (1964), 340-368. Google Scholar

[8] 8. Szász, Gabor, Introduction to lattice theory, Academic Press, New York, 1963. Google Scholar

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