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On the greatest and least elements in the set of semistandard tableaux of given shape and weight

We give three algorithms to construct a semistandard tableau of given shape and weight, where the weight is a composition which is not necessarily a partition. With respect to a natural partial order on the set of semistandard tableaux, we show that the set of semistandard tableaux of given shape and weight has a unique greatest element and a unique least element. Two of our algorithms give each of these elements.

preprint2015arXivOpen access
Akihiro MunemasaMinwon Na
math.CO
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Akihiro MunemasaMinwon Na

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