# Questions tagged [co.combinatorics]

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

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### Partity of partitions with distinct parts of parts $>1$

This question is motivated by my earlier (unanswered) MO post. The number of partitions into distinct parts is generated by $\sum_{n\geq0}Q(n)x^n=\prod_{k\geq1}(1+x^k)$. Focusing on parity of ...
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### Sufficient criterion for unit distance graphs

There are many necessary criteria for a graph to be a unit distance graph. For example, it must not have $K_4$ as a subgraph etc. Can we find some sufficient criterion for a graph to be a unit ...
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### Is the number of words finite, when you don't know how to count?

This question is inspired by this one: Can you do math without knowing how to count? Let $M_2$ be the set of words constructed by concatenation of the letters $a_1$ and $a_2$, with : (*) : for any $x$ ...
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### n sets, each is large, the intersection of every three is small, what is the size of the union?

Let $A_1, A_2, \ldots, A_n$ be $n$ sets such that: (1) for each $i\in [n]$, $\frac{n}{3}\leq |A_i|\leq n$; (2) for any $1\leq i<j<k\leq n$, $|A_i\cap A_j\cap A_k|\leq a$, where $a$ is a constant ...
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