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   Number of skew polyominos
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   Author  Topic: Number of skew polyominos  (Read 4834 times)
howard roark
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Number of skew polyominos  
« on: Dec 8th, 2008, 11:31pm »
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How many skew polyominos can be formed with a perimeter of 2n+2
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towr
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Re: Number of skew polyominos  
« Reply #1 on: Dec 9th, 2008, 1:40am »
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What's the definition of a skew polyomino? Because looking at the examples at mathworld one could be led to believe the answer is 1 for even n4 and 0 otherwise (i.e. both sides need to be extended with one square every time).
« Last Edit: Dec 9th, 2008, 1:41am by towr » IP Logged

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howard roark
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Re: Number of skew polyominos  
« Reply #2 on: Dec 9th, 2008, 8:23am »
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A polyomino is a set of squares connected by their edges. A skew polyomino is a polyomino such
that every vertical and horizontal line hits a connected set of squares and such that the successive columns of squares from left to right increase in height—the bottom of the column to the left is always lower or equal to the bottom of the column to the right. Similarly, the top of the column to the left is always lower than or equal to the top of the column to the right.
 
Find the number of skew polyominos that have a perimeter of 2n + 2. Note that it is the perimeter that is fixed—not the number of squares
in the polyomino.
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howard roark
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Re: Number of skew polyominos   Untitled.jpg
« Reply #3 on: Dec 9th, 2008, 3:36pm »
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I am attaching a picture to make it more clear
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howard roark
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Re: Number of skew polyominos  
« Reply #4 on: Dec 9th, 2008, 3:37pm »
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Don't count them in the figure.... That might give a very big hint
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ThudnBlunder
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Re: Number of skew polyominos  
« Reply #5 on: Dec 9th, 2008, 3:57pm »
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on Dec 8th, 2008, 11:31pm, hoogle wrote:
How many skew polyominos can be formed with a perimeter of 2n+2

F(n) Grin
 
No? OK, try .....C(n) Tongue
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howard roark
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Re: Number of skew polyominos  
« Reply #6 on: Dec 9th, 2008, 6:23pm »
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Quote:
F(n)  
 
No? OK, try .....C(n)  

 
Smiley
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howard roark
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Re: Number of skew polyominos  
« Reply #7 on: Dec 9th, 2008, 6:39pm »
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@Thudanblunder
 
How?
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howard roark
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Re: Number of skew polyominos  
« Reply #8 on: Dec 9th, 2008, 11:06pm »
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Explaining how you arrived at an answer is more valuable than the answer itself.
 
Let us all follow the rules of the forum
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Re: Number of skew polyominos  
« Reply #9 on: Dec 10th, 2008, 12:34am »
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That figure seems to count a lot of polyominals double where the only difference is rotation. Like the first and last, or second and third, for n=3.
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