Conjectures involving arithmetical sequences

By Zhi-Wei Sun. 2012

49 citations recorded by the source corpus.

We pose thirty conjectures on arithmetical sequences, most of which are about monotonicity of sequences of the form $(\root n\of{a_n})_{n\ge 1}$ or the form $(\root{n+1}\of{a_{n+1}}/\root n\of{a_n})_{n\ge1}$, where $(a_n)_{n\ge 1}$ is a number-theoretic or combinatorial sequence of positive integers. This material might stimulate further research.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7358b27dad170cf0098c6b3545476f41ee4f92b7

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In Algebra and Number Theory

1. Igor Pak
2. Stephen Desalvo

In Discrete Mathematics and Combinatorics

1. Igor Pak
2. Stephen Desalvo
3. Shelly Garion
4. Aner Shalev

In Geometry and Topology

1. Igor Pak
2. Stephen Desalvo

Citations in the corpus

• Log-concavity of the partition function (2013, background): “In [24] (see also [23]), Sun conjectures that {r(n)} is log-concave for n ≥ 60.”