Unanswered Questions
3,131 questions with no upvoted or accepted answers
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5 player round-robin tournaments
Is there any literature on the order structure coming from round-robin tournaments? I play games on littlegolem and the tournaments are mostly 5x5 round-robins. I noticed at the end, after sorting ...
- 22.7k
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719
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Decomposing max-convolution of sum of functions ?
Hello.
$R, F_1, F_2, F_3$ are random (not-convex, not-concave) 2D matrices of size 100x100.
$R$ is a linear combination of $F_1, F_2, F_3$.
Explicitly, $R = w_1 F_1 + w_2 F_2 + w_3 F_3$
where $w_1,...
- 33
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119
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A search for optimal order ideals
At the behest of Gerhard Paseman I'll describe the problem that I alluded to in
name for a partial order.
Let $M = M(\infty)$ denote the set of all finite subsets of the positive integers $\mathbb{N}$...
CommunityBot
- 1
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372
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Showing that Paley Graphs are Edge-Transitive
I would like to show that Paley graph are rank $3$ graphs (i.e. Vertex-Transitive, Edge-Transitive and Non-Edge-Transitive).
Showing that they are vertex transitive is easy - every $x \mapsto x+k$ is ...
- 399
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188
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Generate combinations with repeated symbols?
I would like to generate fixed size sequences contained a fixed number of repeated symbols.
For example how to generate sequences of size N containing exactly p symbols of one type q symbols of ...
- 121
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251
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Fast removal of weighted edges in a graph in a way such that all shortest paths are preserved
This problem is analogous to fast removal of the minimum number of edges in a weighted graph such that if the graph were to be drawn on paper with edge lengths linear in proportion to their weights, ...
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562
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Proof of Upper bound of price of anarchy in local connection game
I am looking at the work by Fabrikant "On a Network Connection Game" (http://webcourse.cs.technion.ac.il/236620/Spring2005/ho/WCFiles/FLMPS_netDesign.pdf). This work presents a game-theoretic ...
CommunityBot
- 1
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276
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12 and 13-bit balanced Gray codes
I am trying to find a transition sequence for both 12 and 13 bit balanced Gray codes. I know there are some excellent papers on the topic of deriving these sequences available on the internet, but I ...
- 425
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316
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Estimating a multinomial sum
I have the following sum
\begin{equation}
\sum_{r_1=q+1}^{\tau}\dots\sum_{r_\lambda=q+1}^{\tau}{\tau\choose r_1,\dots,r_\lambda,\tau-r_1-\dots -r_\lambda} (\Lambda-\lambda)^{\tau-r_1-\dots-r_\lambda}
\...
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153
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Finding the bottleneck in a chain of functions
I have a problem that involves finding a bottleneck. It appears to me to be a linear bottleneck assignment problem, but recognizing (and solving) such problems is far outside my area of expertise. If ...
- 4,912
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189
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Packing Icons Onto A screen
You are trying to pack icons onto a screen that is divided into n horizontal rows of uniformly varying size. The rows narrow by a fixed ratio as one goes up the screen from the bottom. Since the icons ...
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1
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340
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Log associahedra and log noncrossing partitions--raising ops and symmetric function theory for $A_n$ (references)
Where do the following three sets $[LA]$, $[ILA]$, and $[LN]$ of partition polynomials appear in the literature?
There are two sets of partition polynomials, not in the OEIS, that serve as the ...
- 10.2k
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1
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120
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Recognizing perfect Cayley graphs as tensor products
It is known (and can easily be seen) that a unitary Cayley graph on $n=\prod_ip_i$, ($p_i$ distinct primes) vertices with $n$ square-free can be recognized as the tensor product of the graphs $K_{p_i}$...
CommunityBot
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425
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Efficient isomorphic subgraph matching with similarity scores
I'm a computer vision PhD student, and I'm looking for an efficient approximation to the following problem, which could end up helping in image to image matching. Failing that, pointers to relevant ...
- 4,589
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2
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741
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Number of Dyck paths with k returns and b peaks
The number of Dyck paths from the origin to $(2n,0)$ which touch the $x$-axis $k+2$ times ($k$ internal touches) is given by
$$\frac{k}{2n-k}{2n-k \choose n}.$$
The number of Dyck paths from the ...
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