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Results tagged with co.combinatorics
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user 7089
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
7
votes
1
answer
431
views
Number of unique sortings of subset-sums
Take the set $A_n=\{a_1,...,a_n\}$. Let $S_n$ be the set of subset-sums of $A_n$. (The subset-sum of the empty set is assumed to be zero.) Assume that there are $2^n$ unique members of $S_n$. How many …
- 2,649
5
votes
1
answer
196
views
A nowhere-zero point in a linear mapping conjecture
I found a very interesting problem in the Open Problem Garden, which I am surprised is not as well-known as I would think it would be:
Prove that If $p>3$ is prime and $A$ is an invertible $n \times n …
- 2,649
13
votes
1
answer
655
views
Frankl's conjecture restricted to finite topological spaces
A finite topological space is a finite family of finite sets that is closed under both union and intersection.
Frankl's conjecture states that for any finite union-closed family of finite sets, othe …
- 2,649
3
votes
0
answers
130
views
Graeco-Latin squares and outer-automorphisms
It is well known that $n=6$ is the only number greater than two in which there is no Graeco-Latin square of order $n$. It is also well known that $n=6$ is the only number greater than two in which the …
- 2,649