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4
votes
0answers
112 views

Partitions of numbers with restrictions on repetitons

I have a question about restricted partitions of numbers: For $n$ and $k$ positive integers let $M$ be the multiset in which each positive integer less than n appears exactly $k$ times. I want to ...
3
votes
0answers
100 views

Are irrational multiples of central sets again central?

Let me begin by giving the relevant definitions. A set $A \subset \mathbb{N}$ is said to be central if and only if there exists a topological system $(X,T)$ (with $X$ a compact metric space, $T$ a ...
14
votes
5answers
1k views

Category Theory and Ergodic Theory

I am very much interested in finding out about any category theoretical work on dynamical systems and on ergodic theory. On the face of it, it seems that a categorical language can go a long way, at ...
6
votes
2answers
245 views

Repeatedly indexing into an $\infty$-sequence of integers

Suppose one has in hand an infinite sequence $s$ of distinct natural numbers, for example, $$s=s_1=(1, 3, 5, 7, 9, 11, 13, 15, 17, 19,\ldots) \;.$$ So this sequence can be considered an injection ...
8
votes
3answers
1k views

Gauss sum (with sign) through algebra

Let $p$ be an odd prime, and $\zeta$ a primitive $p$-th root of unity over a field of characteristic $0$. Let $G = \sum\limits_{j=0}^{p-1} \zeta^{j\left(j-1\right)/2}$ be the standard Gauss sum for ...