arXiv subjects
Publications and source records attributed to Minwon Na.
We take an elementary approach to derive a generalization of Kunth's formula using Lassalle's explicit formula. In particular, we give a formula for the Kostka numbers of a shape $\mu\vdash n$ and weight $(m,1^{n-m})$ for $m=3,\;4$.
The aim of this paper is to give a corrected bijective proof of Vershik's relations for the Kostka numbers. Our proof uses insertion and reverse insertion algorithms, as in the combinatorial proof of the Pieri rule.
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.