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I have a set of digits. For example, 3 1s, 2 2s, 10 3s, ...

With this available digits how do I create a palindromic table of fixed (nxm) matrix where each row and column is palindromic?

For a linear structure, I can simply do mirror reflection to get a palindrome. But unable to come up with a stretagies to form a palindromic matrix using ALL of the provided digits.

Any help is much appreciated.

user3243499
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1 Answers1

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The general entries in the matrix fall into groups of $4$ that must be identical because of the palindromic symmetry. If $n$ or $m$ is odd, the entries in the central rows or columns fall into groups of $2$; and if both $n$ or $m$ are odd, the central entry forms a singleton by itself. All this depends only on $n$ and $m$, so without looking at your digits, you know how many groups of $4$ identical digits and how many groups of $2$ identical digits you need.

You can start by assigning the digits of which you have at least $4$ to the groups of $4$ entries, and then assign the digits of which you have at least $2$ left to the groups of $2$ entries. Your digit counts must all be even, except if both $m$ and $n$ are odd, in which case exactly one of your digit counts must be odd. So in your example, we can tell from your digit counts that $n$ and $m$ must be odd and that the central entry in the matrix will be a $1$. (This is assuming that you require all the available digits to be in the matrix.)

joriki
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