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Results tagged with co.combinatorics
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user 127690
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
9
votes
Accepted
Are there only two solutions for $1+3+9+...+3^m=2^n$
Yes, those are the only solutions. To see this note that $$1+3+9+27 \cdots 3^m = \frac{3^{m+1}-1}{2}.$$
So we are looking for solutions of $\frac{3^{m+1}-1}{2}=2^n$, or equivalently looking for soluti …
- 6,969
20
votes
3
answers
1k
views
The Angel and Devil problem with a random angel
In the classic version of Conway's Angel and the Devil problem, an angel starts off at the origin of a 2-D lattice and is able to move up to distance $r$ to another lattice point. The devil is able t …
- 6,969
5
votes
1
answer
256
views
Is a weak version of the three sets Lemma provable in ZF?
The Three Sets Lemma is the following Lemma:
Lemma: Let $f(x)$ be a function from $X$ to $X$ where $f(x)$ has no fixed points. Then there exists a partition of $X$ into three disjoint sets $X_1$, $X_2 …
- 6,969
12
votes
The Stable Set Conjecture
There is a subsequent 1989 paper by Hildebrand, "On integer sets containing strings of consecutive integers" which shows that the if the set satisfies $d(A)>\frac{k-2}{k-1}$ then the conjecture holds …
- 6,969
5
votes
Open problems which might benefit from computational experiments
This answer is similar in style to Marco Ripa's concerning a specific preprint. In this preprint by me and Tim McCormack, Weighted Versions of the Arithmetic-Mean-Geometric Mean Inequality and Zaremba …
11
votes
5n+1 sequence starting at 7
As far as I understand it, under the current state of things we cannot prove that any orbit of 5k+1 diverges. In fact, as far as I'm aware we cannot even prove that there exists an odd $a>1$ such that …
- 6,969