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Results tagged with co.combinatorics
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user 20343
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
204
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Are the primary parallelotopes classified? (equivalently, Voronoi cells of lattices)
A primary parallelohedron is a polyhedron that can fill space with infinite translated copies.
It is known (e.g., Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, pp. 29-30, 1973; or, Tu …
- 1,441
7
votes
2
answers
547
views
Kissing Number of Spheres in Non-Euclidean Geometry
There has been much work done on the kissing number problem (of determining the greatest number of congruent spheres which can touch a single sphere in a packing) in Euclidean space for dimensions $1$ …
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4
votes
2
answers
356
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Finding the order of a flip graph and how it relates to all possible triangulations of a graph
I've recently run into the following problem:
Given a planar graph, how many possible triangulations are there?
I am using triangulations in the normal sense when applied to anything in geometri …
- 1,441
3
votes
1
answer
723
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Klein Bottle exception to the Heawood Conjecture [duplicate]
Possible Duplicate:
The Klein bottle and the Heawood Conjecture
It is well known that the Heawood Conjecture states that the bound for the number of colours which are sufficient to colour a m …
- 1,441
2
votes
2
answers
281
views
On the Combinatorial Classification of Modal Kripke Frames
We have that S5 modal logic is characterized by the modal axioms $K$, $M$ (reflexive), $4$ (transitive), and $B$ (symmetric). That is, an equivalence relation on a set of possible world (which can be …
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1
vote
1
answer
497
views
Does the Hardy-Ramanujan Asymptotic Formula Partition Sets or Integers?
From "Models and Games" by Jouko Vaananen (Cambridge studies in advanced mathematics), I quote
The Hardy-Ramanujan asymptotic formula says that the number of equivalence relations on a fixed set o …
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1
vote
1
answer
133
views
Generalizing the internal angle of a graph in $\mathbb{E}^2$ to $\mathbb{S}^2$
I am currently working on research involving packing problems and am finding myself needing the tools from Combinatorial Geometry (in particular, I've been reading Pach and Agarwal's book on the subje …
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0
votes
Accepted
On the Combinatorial Classification of Modal Kripke Frames
I happened to end up writing a paper which answered my question if anyone else is ever interested in this topic or comes across this question:
"On Generalizing a Temporal Formalism for Game Theory to …
- 1,441
0
votes
1
answer
145
views
Asymptotics of the Number of Non-Isomorphic Equivalence Relations and the Number of Non-Isom...
The number of non-isomorphic equivalence relations on a set of $n$ elements is the partition function
$$p(n) =\frac{1}{\pi\sqrt{2}} \sum_{k=1}^{\infty} \sum_{h=1}^{k} \delta_{\gcd(h,k),1} \text{exp}\l …
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