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.}