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Results tagged with co.combinatorics
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user 63938
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
13
votes
1
answer
689
views
Göbel's correspondance between rooted trees and natural numbers
In the paper On a 1-1-correspondence between rooted trees and natural numbers by F. Goebel, a correspondence between natural numbers and rooted tree was established via prime factorization.
He defines …
- 155
14
votes
2
answers
960
views
Conjecture on maximum of symmetric combinatoric function
A curious symmetric function crossed my way in some quantum mechanics calculations, and I'm interested its maximum value (for which I do have a conjecture).
(The question was first asked at math.SE, …
- 155
9
votes
1
answer
382
views
Why is the number of Perfect Matchings in a triangular grid equivalent to the number of Roya...
The sequence A006318 at OEIS stands for the Schröder numbers.
They describes the number of lattice paths from the southwest corner $(0,0)$ of an $n\times n$ grid to the northeast corner $(n,n)$, …
- 155
21
votes
1
answer
1k
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Smallest known counterexamples to Hedetniemi’s conjecture
In 2019, Shitov has shown a counterexample (Ann. Math, 190(2) (2019) pp. 663-667) to Hedetniemi’s conjecture,
$$\chi(G \times H)=\min(\chi(G),\chi(H))$$
where $\chi(G)$ is the chromatic number of the …
- 155
5
votes
0
answers
157
views
Dirichlet eta function and Stirling Permutations
The Stirling permutations of order $k$ is a permutation of the multiset $1, 1, 2, 2, ..., k, k$. The Dirichlet $\eta$-function is a function closely related to the Riemann $\zeta$-function.
According …
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11
votes
1
answer
816
views
Graphs with only disjoint perfect matchings, with coloring
The following purely graph-theoretic question is motivated by quantum mechanics.
Definitions: A bi-colored graph $G$ is an undirected graph where every edge is colored. An edge can either be monochro …
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32
votes
0
answers
3k
views
Vertex coloring inherited from perfect matchings (motivated by quantum physics)
Added (19.01.2021): Dustin Mixon wrote a blog post about the question where he reformulated and generalized the question.
Added (25.12.2020): I made a youtube video to explain the question in detail.
…
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