论文标题
在Okounkov-Olshanski公式上，用于标准偏斜形状的标准图表
On the Okounkov-Olshanski formula for standard tableaux of skew shapes
论文作者
论文摘要
经典的钩长公式计算直形形状的标准表格数量。 1996年，Okounkov和Olshanski发现了一个偏斜形状的标准年轻tableaux数量的正式。 We prove various properties of this formula, including three determinantal formulas for the number of nonzero terms, an equivalence between the Okounkov-Olshanski formula and another skew tableaux formula involving Knutson-Tao puzzles, and two $q$-analogues for reverse plane partitions, which complements work by Stanley and Chen for semistandard tableaux.我们还对公式进行了几个重新制定，其中包括两个在Naruse最近出现的倾斜tableaux公式中出现的激发图。最后，对于厚的锯齿形形状，我们表明，非零项的数量由基因科奇数的决定因素给出，并在这些形状的标准tableaux数量上通过Morales-Pak-Panova改进了已知上限。
The classical hook length formula counts the number of standard tableaux of straight shapes. In 1996, Okounkov and Olshanski found a positive formula for the number of standard Young tableaux of a skew shape. We prove various properties of this formula, including three determinantal formulas for the number of nonzero terms, an equivalence between the Okounkov-Olshanski formula and another skew tableaux formula involving Knutson-Tao puzzles, and two $q$-analogues for reverse plane partitions, which complements work by Stanley and Chen for semistandard tableaux. We also give several reformulations of the formula, including two in terms of the excited diagrams appearing in a more recent skew tableaux formula by Naruse. Lastly, for thick zigzag shapes we show that the number of nonzero terms is given by a determinant of the Genocchi numbers and improve on known upper bounds by Morales-Pak-Panova on the number of standard tableaux of these shapes.
