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Results tagged with co.combinatorics
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user 5903
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
votes
Countable support product of Sacks forcings and selective ultrafilters
I'm not allowed to comment yet but your question looks equivalent to having the set $A$ in $\mathrm{HL}_\omega$ (see Laver's paper) belong to the ultrafilter. I do not recall how flexible Laver's proo …
- 11.4k
7
votes
Accepted
Sunflowers in maximal almost disjoint families
The following is a ZFC example, due to Michael Hrušák, of a MAD family without sunflowers of
cardinality $3$.
Start with the standard AD family $\mathcal{B}=\{B_f:f\in{}^\omega2\}$ of
branches through …
- 11.4k
1
vote
Accepted
Compactness of Hadwiger number
Assume $K_n$ is a minor of $G$. Each vertex of $K_n$ corresponds to a connected subset of vertices of $G$ as it can only have been obtained by contracting edges. Each edge of $K_n$ can only have been …
- 11.4k
2
votes
Putting $\omega$ into $\alpha$ boxes where $\alpha \in \big(\omega\cup\{\omega\}\big)\setmin...
The method from this answer leads to $B_\alpha\le\binom{\alpha+1}{2}$ for finite $\alpha$.
Split $\omega$ into $\alpha+1$ infinite sets, say $X_i=\{n:n\equiv i \pmod{\alpha+1}\}$. For each $p\in[\alph …
- 11.4k