Abstract
A bijective proof for Stanley's hook-content formula for the generating function for column-strict reverse plane partitions of a given shape is given that does not involve the involution principle of Garsia and Milne. It is based on the Hillman-Grassl algorithm and Schützenberger's \emphjeu de taquin.
Highlights
The purpose of this article is to give a bijective proof for Stanley’s hook-content formula [15, Theorem 15.3] for a certain plane partition generating function
We discuss some related bijections. It is there where we explain how our bijection described in Section 2 can be used to provide a much simpler bijection between the sets that Remmel and Whitney use in their bijective proof [10] of Theorem 1
There should be nice combinatorial proofs that explain these forms of the formulas
Summary
The purpose of this article is to give a bijective proof for Stanley’s hook-content formula [15, Theorem 15.3] for a certain plane partition generating function. ✄ ✝✟✄✖✱✠ ☛✒✑✓✑✒✑✓☛✌✄✎✱✲✴✳✒✗ ✄✎✵✱ ✶ The conjugate of is the partition where is the length of the -th column in the Ferrers. We label the cell in the -th row and -th column of (the Ferrers diagram of) by the pair. If we write we mean ‘ is a cell of ’. ✸ ✸ ✸ ✸ ✸ the same row as and to the right of , or in the same column as and below , included. ❈ ✼ ✸❉☎❊✝✮✬✔☛✾✶✿✗ ✄ ✶ ❁ ✬ of a cell of is. 1365–8050 c 1998 Maison de l’Informatique et des Mathematiques Discretes (MIMD), Paris, France
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