Unanswered Questions
3,201 questions with no upvoted or accepted answers
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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 ...
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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 ...
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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 ...
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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
answer
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 ...
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votes
1
answer
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 $K_{p_i}$...
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1
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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 ...
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votes
2
answers
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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1
answer
821
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How to calculate determinants of such types?
Consider next determinant that we want to expand around $h=1$
\begin{eqnarray}
Z_q \ = \ h^{N N_f} \ \ \left ( \prod_{n=1}^{N} \ \sum_{l_n=0}^{N_f -q} \ h^{2l_n+q} \ \binom{N_f}{l_n} \right ) \ \...
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1
answer
65
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A follow-up question in a proof in a paper on complete multipartite graphs
A follow-up question from the following article/paper:
"Proof of a conjecture on distance energy change of complete multipartite graph due to edge deletion"
by Shaowei Sun and Kinkar Chandra ...
-1
votes
1
answer
208
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Perfect Cayley graphs for abelian groups have $\frac{n}{\omega}$ disjoint maximal cliques
Let $G$ be a perfect/ weakly perfect Cayley graph on an abelian group with respect to a symmetric generating set. In addition let the clique number be $\omega$ which divides the order of graph $n$. ...
-1
votes
1
answer
96
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Tuza theorem to prove vizing theorem
The Tuza theorem states that every graph with no cycle congruent to 1 mod $k$ is $k$ colorable. Now, the line graph of any simple graph of maximum degree $d$ is seen to posess the property that it has ...
-1
votes
1
answer
389
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Odd & even permutations and unit fractions
One more motivated by recent questions of Zhi-Wei Sun.
Let $S_n$ be the group of permutations of $\{1,2,\ldots, n\}$.
Is it true that, for every $n \ge 8$, there is at least one even permutation $\...
-1
votes
1
answer
76
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Transforming random variables for having good property?
For arbitrary functions $A$ and $B$ and independent random variables $X$ and $Y$, assume that
\begin{align}
\Omega&\triangleq \{(x,y): A(x,y)=1\},\\
\Lambda&\triangleq \{x: B(x)=1\}.
\end{...