Losy
Reputation
Top tag
Next privilege 100 Rep.
Edit community wikis
 Apr 27 comment Number of cycles in a grid such that each cycle traverse all the lines WooooW! thanks a lot... I hope it works. Apr 27 comment Number of cycles in a grid such that each cycle traverse all the lines Exactly. For $2n=8$ there are 26 different cycles and for $2n=10$ there are 240 different cycles. And... Apr 27 comment Number of cycles in a grid such that each cycle traverse all the lines No dear. for $n=2$ you have only one circuit, why 4? $n=2$ the grid has 4 intersection points and 4 bounded segments, and then it has just one cycle. Apr 27 comment Number of cycles in a grid such that each cycle traverse all the lines Then the problem is rather easy, and I know the solution and the exact number. Removing the intersections is worthy. Apr 27 comment Number of cycles in a grid such that each cycle traverse all the lines Absolutely! How many different circuits of length $2n$ are in the grid. This makes the problem rather hard. But because of the well shaped appearance of the grid, I want to see if any one has any suggestion for counting these circuits or an upper/lower bound for them. Although $(n-1)!$ is known as a lower bound. Apr 26 asked Number of cycles in a grid such that each cycle traverse all the lines Apr 26 accepted Number of $(0,1)-$matrices with exactly two $1$'s in each row and column Apr 25 asked Number of $(0,1)-$matrices with exactly two $1$'s in each row and column Apr 25 accepted Partition an integer $n$ by limitation on size of the partition Apr 25 awarded Scholar Apr 25 accepted Decomposition by subtraction Apr 16 asked Partition an integer $n$ by limitation on size of the partition Apr 16 awarded Student Apr 16 comment Decomposition by subtraction Both comments were extremely helpful. Now, is there any idea about how I can count those decompositions with exactly $i$ members? for example there are $\lfloor \frac{n}{2} \rfloor$ decompositions for $n$ with exactly two members, for 13 we have $\{10,3\}$,$\{9,4\}$,.... What about the number of decompositions of $n$ with exactly $i$ members, members are greater than two? It is clear that because the members are at least three, $i$ is smaller than $\lfloor \frac{n}{3} \rfloor$. Apr 16 awarded Editor Apr 16 revised Decomposition by subtraction deleted 59 characters in body; deleted 71 characters in body Apr 16 asked Decomposition by subtraction