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Results tagged with co.combinatorics
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user 22971
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
33
votes
Accepted
Why is the Frankl conjecture hard?
(Migrated by request from the comments.)
Bruhn and Schaud's (2013) The journey of the union-closed sets conjecture provides a rather readable write-up. Particularly relevant is the section Obstacles …
- 7,831
3
votes
A puzzle with some jumping frogs
Edit: As pertains to UPDATE 2, the post below gives references to settle the case of $\ell = 1$.
This is a bit long for a comment, but I thought it worthwhile in case the following is non-obvious:
…
- 7,831
1
vote
Accepted
Is there a function that determines the rank of a multiset after inserting another element?
Start by attempting the problem for ordered multisets; once you have found a formula, go back and adjust for non-ordered multisets (if you so desire).
First, re-stating your ranks for ordered multise …
- 7,831
6
votes
1
answer
426
views
Crossing number of the Grötzsch graph
Related wikipage: http://en.wikipedia.org/wiki/Gr%C3%B6tzsch_graph
Is the crossing number of the Grötzsch graph known? I have heard it conjectured to be 5 (certainly it is no greater), but came up em …
- 7,831
17
votes
Accepted
Colourings of $\mathbb Q\times \mathbb Q$ in three colours
Here are, at least, some remarks about your question that will not fit as a comment:
You request parenthetically that you would like to exclude "degenerate" colourings that use almost only two colour …
- 7,831
15
votes
Accepted
Göbel's correspondance between rooted trees and natural numbers
(I see this in the comments, too, but to ensure this has an actual answer...)
Here are the first fifteen natural numbers after drawing an individual line segment (edge and node) beneath the root:
As …
- 7,831
7
votes
Is the Steiner ratio Gilbert–Pollak conjecture still open?
[Since this question has not elicited any other responses over the past two months, I am now migrating my comments to serve as an answer.]
As far as I know, the answer is yes: it's still open. Pollak …
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4
votes
0
answers
228
views
How many arrangements of $n$ points with $k$ edge lengths exist in $d$ dimensions?
[Asking on behalf of a high school mathematics course, but responses written at any level are welcome!]
I was recently reading over a nice puzzle called the four points, two distances problem:
Fi …
- 7,831
7
votes
Accepted
Question about tetrahedron decomposition
In the case where the three parts are each congruent to one another, the answer to your question is no: there is no such decomposition of a tetrahedron.
The terminology needed to find such an answer …
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4
votes
1
answer
325
views
Enumerating subsets with no triple appearing together more than once
This question is motivated by a real-world application related to an art project that involves displaying images, but my search hit a dead end after finding the wikipage about Kirkman systems (other r …
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9
votes
3
answers
1k
views
Intuition Behind a Decimal Representation with Catalan Numbers
From $0 = 0.5 - 0.5 = 0.5 - \sqrt{0.25}$, we can adjust the subtrahend slightly to obtain
$$0.5 - \sqrt{0.249} = 0.001\ 001\ 002\ 005\ 014\ 042\ldots$$
where the decimal representation contains the …
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3
votes
An identity for product of central binomials
I think that this is routine to verify by induction (as Fedor Petrov suggests in a comment). With respect to a response that is "instructional," suppose (or check) that the identity holds when $n = 4$ …
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