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Results tagged with co.combinatorics
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user 10235
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
8
votes
A result from Peter McMullen's thesis
This is theorem 4C6 of Peter McMullen's thesis, "On the Combinatorial Structure of Convex Polytopes", on page 73:
4C6. Theorem. A $d$-polytope $P$ is regular if and only if for each $j = 0, \dots, …
- 590
27
votes
1
answer
2k
views
Solutions to $\binom{n}{5} = 2 \binom{m}{5}$
In Finite Mathematics by Lial et al. (10th ed.), problem 8.3.34 says:
On National Public Radio, the Weekend Edition program posed the
following probability problem: Given a certain number of bal …
- 590
4
votes
Is there any edge- but not vertex-transitive polytope in $d\ge 4$ dimensions?
If you consider a tiling of 3-space to be a 4-dimensional polytope, then the Rhombic dodecahedral honeycomb would work.
Other possibilities are limited by the potential 3-faces.
Because every edge h …
- 590