Combinatorial Identities Involving the Mobius Function
Mohamed El bachraoui, Mohamed Salim
TL;DR
This paper derives new identities and inequalities involving the Möbius function using phi functions for intervals of positive integers, advancing theoretical understanding of number theoretic functions.
Contribution
It introduces novel identities and inequalities for the Möbius function based on interval phi functions, providing new theoretical insights.
Findings
New identities involving the Möbius function
Inequalities established for the Möbius function
Use of phi functions for intervals in proofs
Abstract
In this paper we derive some identities and inequalities on the M\"obius mu function. Our main tool is phi functions for intervals of positive integers and their unions.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · semigroups and automata theory