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Results tagged with co.combinatorics
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user 2386
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
6
votes
1
answer
2k
views
Comparing number of spanning subgraphs
Hi all,
Let be $G_n=(V_n,E_n)$ a finite graph, where
$V_n= \{0,1,\ldots, n\} \times\{0,1,\ldots,n\}$
and $E_n\subset V_n^{(2)}$ is the edge set of the nearest neighbors in the $\ell^1$ norm, that …
- 2,044
5
votes
2
answers
649
views
How many Hamiltonians Paths there are in almost regular graph ?
Let be $G=(V,E)$, where $V=\{1,\ldots,n\}$ and $E=\{\{i,j\}\subset V;|i-j|\leq k\}$ and $k<n$.
For which values of $k\geq 2$, can we count explicitly the number of Hamiltonian paths in $G$ ?
- 2,044
9
votes
Some models for random graphs that I am curious about
(It is not an answer but I put it here because I am having problems to post it in the comments)
Hi Gil, thinking about the question 3 comes in my mind the Gibbs measures. It does not maximize the en …
- 2,044
11
votes
3
answers
874
views
Exponential bounds for the number of lattice animals with a given boundary.
Hi all,
I am doing a work in collaboration with other mathematicians about phase transition in the Ising model and we need to know if exponential upper bounds exist for the number of lattice animals …
- 2,044
2
votes
Bounding sum of multinomial coefficients by highest entropy one
Hi Yaroslav, With the additional hypothesis you are considering, I guess that the inequality can be proved following the text that you linked.
Fix any probability vector $(p_1,\ldots,p_k)$ and consi …