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Results tagged with co.combinatorics
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user 106046
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
11
votes
Accepted
A remarkable identity involving $\chi^2$ random variables
I think I found an elementary proof of Question 2/3 for arbitrary probability distributions. In fact, it is not required that the components in the sums are squares, but general i.i.d. non-negative ra …
- 1,095
3
votes
0
answers
179
views
Direct proof for average property of union-closed family
Let $\mathcal{A} \subset 2^{\{1, 2, \dots, n\}}$ be a union-closed family of sets (i.e., for any $A, B \in \mathcal{A}$, also $A \cup B \in \mathcal{A}$). In this paper it is established that
$$
\sum_ …
- 1,095
2
votes
Accepted
The largest Wasserstein distance to uniform distribution among all probability distributions...
I think I have an answer for the case p = 1, K = 2. I write "I think" because my computation does not coincide with the example values for $N=4$ posted earlier by OP in a comment, but I really cannot …
- 1,095
1
vote
0
answers
48
views
Inequality between union-closed families of sets and corresponding upward-closed families
This question is about an inequality for union-closed families of sets related to Frankl's conjecture and a result by Reimer. It relates the union-closed families and corresponding upward-closed famil …
- 1,095