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Abstract: The main topic of this contribution is the problem of counting square-free numbers not exceeding $n$. Before this work we were able to do it in time (Comparing to the Big-O notation, Soft-O ...
An Algorithm to Generate Square-Free Numbers and to Compute the Moebius Function
Mobius function square-free numbers zeta function Riemann hypothesis
2011/9/19
Abstract: We introduce an algorithm that iteratively produces a sequence of natural numbers k_i and functions b_i. The number k_(i+1) arises as the first point of discontinuity of b_i above k_i. We de...
Depth and minimal number of generators of square free monomial ideals
Monomial Ideals Depth Stanley depth Commutative Algebra
2011/9/5
Abstract: Let $I$ be an ideal of a polynomial algebra $S$ over a field generated by square free monomials of degree $\geq d$. If $I$ contains more monomials of degree $d$ than $(d+1)/d$ of the total n...
Circular words are cyclically ordered finite sequences of letters. We give a computer-free proof of the following result by Currie: square-free circular words over the ternary alphabet exist for all l...
On the Symmetry of Square-Free Supported Arithmetical Functions in Short Intervals
Symmetry Square-free short intervals
2008/6/27
On the Symmetry of Square-Free Supported Arithmetical Functions in Short Intervals.