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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

0 votes
0 answers
81 views

Constructing set with maximal independent subset

What is the minimal $m$ such that there exists a set $A = \{a_1,...a_n\}$ of vectors : $a_i \in \{0,1\}^m$ ($n$ is given) such that every subset of vectors of size $k$ is independent, but only with sc …
15 votes
7 answers
1k views

Examples of proofs by making reduction to a finite set [closed]

This is a very abstract question, I hope this is appropriate. Suppose $T$ is some claim over some infinite set $A$, for example, let $A$ be the set of all loopless planar graphs, and $T$ be the claim …