Covering algebras and \(q\)-binomial generating functions (Q1322175)

In this paper the authors, R. Davis and C. Wagner, study the reduced covering algebras of binomial lattices by using the theory of reduced incidence algebras of binomial posets, and construct an isomorphic algebra of arithmetic functions called the Newton algebra. It is shown that for modular binomial lattices in which length two intervals contain more than one atom, the Newton algebra may be construed as an algebra of formal \(q\)-binomial series.