All Questions
Tagged with ds.dynamical-systems co.combinatorics
14 questions with no upvoted or accepted answers
57
votes
0
answers
3k
views
On the first sequence without triple in arithmetic progression
In this Numberphile video (from 3:36 to 7:41), Neil Sloane explains an amazing sequence:
It is the lexicographically first among the sequences of positive integers without triple in arithmetic ...
9
votes
0
answers
225
views
On the first sequence without collinear triple
Let $u_n$ be the sequence lexicographically first among the sequences of nonnegative integers with graphs without collinear three points (as for $a_n=n^2$ or $b_n=2^n$). It is a variation of that one.
...
7
votes
0
answers
429
views
Dynamics of a curious bijection of $\mathbb N$
The two sequences A48680 and A48679 of the OEIS define two mutually inverse bijections on the set of all strictly positive natural numbers given (for the comfort of the reader) as follows:
Given an ...
- 17.9k
7
votes
0
answers
1k
views
Absolute oscillator in Langton's Ant
We have a simple (or single) block of Langton's Ants colony which includes two ants looking in the same direction. Their positions can be interpreted as knight's walk. The distances between each next ...
- 303
6
votes
0
answers
690
views
Unique Nash equilibrium games
Multicast network design game is a special case of a general network design game (http://www.cs.cornell.edu/home/kleinber/focs04-game.pdf) in which there is a target vertex $t$ and $n$ rational ...
- 399
3
votes
0
answers
124
views
Oscillator in Langton's ant
First of all, see Langton's ant Wikipedia page.
If we place a pair of ants looking north (using Golly or any another prog) on the coordinates $(x_1,y_1)$ and $(x_2,y_2)$ under the conditions:
$p=|x_1-...
- 4,938
3
votes
0
answers
81
views
Size of the kernel (minimal ideal) of a finite semigroup
Let $A$ be an irreducible nonnegative $N\times N$ integer matrix with constant row sum $D$. Let $A_1, \dots, A_D$ be nonnegative integer matrices, each with constant row sum $1$, such that $\sum_k A_k ...
- 695
3
votes
0
answers
98
views
Does singularity confinement imply a fixed pattern of irreducible factors?
Consider a rational map
$f \colon (x_1,\ldots,x_n) \mapsto (P_1(x_1,\ldots,x_n),\ldots,P_n(x_1,\ldots,x_n))$, where the $P_i$ are rational functions. Via iteration this map defines a discrete ...
- 24.2k
3
votes
0
answers
56
views
Self-map of a set for which the sizes of fibers of iterates are given by polynomials
I am interested in functions $f\colon X\to X$ (where $X$ is some countable set) such that for every $x \in X$ there exists a polynomial $P_x$ such that $\#(f^k)^{-1}(x)=P_x(k)$ for all $k \geq 1$.
...
- 24.2k
3
votes
0
answers
123
views
Irregularly Intertwined Linear Recursions: Other References?
I was wondering if anyone had run across the following notion of intertwined linear recursions. I'm looking for references, or even a standard name. (I know one source, which is the genesis of this ...
- 47.4k
3
votes
0
answers
233
views
How many set partitions on a big cube’s boundary arise from cubomino decompositions of the solid cube?
Introduction. This is a counting question about configurations that can appear on the outside of assembled Soma cube-like puzzles. More specifically, it’s about the ways in which the pieces of an ...
- 588
1
vote
0
answers
125
views
Minimal period for a bounded Langton's ant moving on a tessellation
We consider Langton's ant on the 2D plane, but we replace the square lattice by a Voronoi tessellation obtained from a finite set of points (it could be another tessellation, however directions such ...
- 111
1
vote
0
answers
223
views
Trigonometric semialgebraic conditions for two floors to be unequal [edited]
EDIT: Since posting my original question I have simplified the problem to finding a sufficient condition for $\lfloor \frac{a}{\phi}\rfloor \neq \lfloor \frac{b}{\phi}\rfloor$ which is trigonometric ...
- 881
0
votes
0
answers
117
views
excplicit formula of iterates of an interval exchange
Let $f$ be an interval exchange transformation of $[0,1]$. Is there an explicit formula giving $f^k(0)$ in function of $k$?
If not, are there particular cases where this formula is simple? (except ...
- 73