# Can an m * n matrix be given Young Tableau property in O(1) space?

If it can be done with heaps why not Young Tableaux? [1]

I know that the analogy is too simplistic but for learning sake, let us consider it.

The only limitation I noticed is that while heaps exhibit local dependencies, Young Tableaux have strong global dependencies. [2]

But independent of this, someone might have already done it. Is it possible and if so, how? If not, give an objective reason why not (possibly with proofs if you can). [3]

[1] Arrays can be given heap property in O(1) space.

[2] The term "local dependencies" as used with reference to heaps is because dependent relationships only spawn between parent and child. In Young Tableaux, dependent relationships spawn across rows and columns. Hence my use of the term "global dependencies".

[3] We all know that opinions will not help so for posterity sake, let’s stick with objective reasons.

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• I am writing an article and I made such a bold statement but cannot back it up which got me stuck so I need help figuring this one out. Thank you for your time. Commented Jul 28 at 6:49
• I am familiar with the definition of Young tabeaux, but I have hard time understanding the question. What do you mean by "giving Young tabeau property" to a matrix? Commented Jul 28 at 12:36
• Turning a matrix into a Young Tableau. In programming we say we have given it a particular property. Technically it is still a matrix but now has a certain property — Young Tableau. Commented Jul 28 at 13:11
• Yes, but which operations are you allowed to use for that? I can turn any matrix into a Young tableau by writing the elements from 1 to $mn$ into the matrix in the right order Commented Jul 28 at 13:14
• I thought so too. But I think that while that is space optimal, it is not time optimal. Nonetheless that answers the question with lingering concern for time complexity. Commented Jul 28 at 17:42