Losy

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seen May 6 '11 at 7:47

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