A class of additive multiplicative graph functions

Some Remarks about Additive and Multiplicative Functions

The present paper contains some results about the classical multiplicative functions (n), a(n) and also about general additive and multiplicative functions. (1) It is well known that n/{n) ^x.) It is known that both fi(x) and fï(x) are strictly inc...

A relation between additive and multiplicative complexity of Boolean functions

In the present note we prove an asymptotically tight relation between additive and multiplicative complexity of Boolean functions with respect to implementation by circuits over the basis {⊕,∧, 1}. To start, consider a problem of computation of polynomials over a semiring (K,+,×) by circuits over the arithmetic basis {+,×} ∪K. It’s a common knowledge that a polynomial of n variables with nonsca...

The Maximum Number of Edges in a Strongly Multiplicative Graph

Additive multiplicative increasing functions on nonnegative square matrices and multidigraphs

It is known that if f is a multiplicative increasing function on N, then either f(n) = 0 for all n∈N or f(n) = n for some ¿0. It is very natural to ask if there are similar results in other algebraic systems. In this paper, we 1rst study the multiplicative increasing functions over nonnegative square matrices with respect to tensor product and then restrict our result to multidigraphs and loopl...

the maximum number of edges in a strongly multiplicative graph

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