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Results tagged with co.combinatorics
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user 8250
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
5
votes
Accepted
Magic $\mathbb{Z}\times\mathbb{Z}$-square
I'll try to show that we can make a square such that all rows and columns give zero sum. (Where "sum" is meant in the sense described in the question.) I.e., this is the answer to the stronger variant …
- 4,713
19
votes
Accepted
"Rocket elements" in bijections $f:\mathbb{N}\to \mathbb{N}$
Choose any infinite set $A\subseteq\mathbb N$ such that $\mu^+(A)=0$. Enumerate both $A$ and $B=\mathbb N\setminus A$ as
\begin{align*}
A&=\{a_1<a_2< \dots < a_n < \dots\}\\
B&=\{b_1<b_2< \dots < b_n …
- 4,713
19
votes
Accepted
Arranging all permutations on $\{1,\ldots,n\}$ such that there are no common points
We are basically looking at the Cayley graph of $S_n$ where the generating set is the set of all derangements. The question is whether this graph is Hamiltonian.
I will quote here a paper by Rasmusse …
- 4,713
4
votes
Accepted
Do monotone functions on the interval have an "Alexander duality" property?
Let us try to construct $S$ which is a counterexample to (B) by transfinite induction. (In the style of just-do-it1 proofs.)
We will use the fact2 that the set $\mathcal M$ of all monotone non-decrea …
- 4,713