The combinatorics behind number-theoretic sieves
Following \textit{G.-C. Rota}'s extension of the Möbius function to a general lattice, described in [Z. Wahrscheinlichkeitstheorie Verw. Geb. 2, 240-368 (1964; Zbl 0121.02406)], the author extends the notions of upper and lower bound sieve to this context. He supplies an extension of Selberg's upper bound sieve to this more general situation. As he notes, the proof in the number-theoretic case carries over almost word for word. A number of situations are described where one hopes that this idea might be applied. No details of any such application are given; the author indicates that he hopes to do this at a later date. A note added in proof acknowledges the earlier paper on the same theme by \textit{R. J. Wilson} [Colloq. Math. Soc. János Bolyai 4, 1141-1149 (1970; Zbl 0213.33203)].
scientific article; zbMATH DE number 1228410
scientific article