# Questions tagged [combinatorial-number-theory]

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8
questions

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votes

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53 views

### Extremal thresholds of balancing integer vectors by linear transformation

Take $v$ to a vector in $\mathbb Z^m$ with entries from $0$ to $2^k-1$ (there are $2^{km}$ possible vectors).
Define $L(v)$ to be difference between the largest and the smallest entries in $v$ and ...

**5**

votes

**1**answer

552 views

### Eulerian ordering of the integers modulo n

Let $n>1$ be an integer. Consider the set $C_n := \{0,1, \dots , n-1\}$.
An Eulerian ordering of $C_n$ is an ordering $r_1, \dots, r_n$ of its elements such that:
$$\forall i \le n \ \forall j&...

**6**

votes

**2**answers

424 views

### Divisibility labeling on a boolean lattice and positive Euler totient

Let $B_n$ be the rank $n$ boolean lattice (i.e. the subset lattice of $\{1,2, \dots , n \}$). Let $\hat{0}$ and $\hat{1}$ be the minimum and the maximum of $B_n$. Let $f: B_n \to \mathbb{N}$ be a ...

**5**

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**0**answers

197 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 ...

**7**

votes

**1**answer

197 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 ...

**17**

votes

**5**answers

2k 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

**2**answers

260 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
$f:...

**11**

votes

**3**answers

2k 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 $...