Some results on hook lengths

✍ Scribed by Joan E. Herman; Fan R.K. Chung

• Book ID: 103058850
• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 652 KB
• Volume: 20
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(77)90040-1

✦ Synopsis

Hill, NJ Iy7973, U.S.A.

A tuhieau is a rectangular array of poiiits with the property that. for all i. the number 4 points in the ith row is greater than or equal to the number of points in the (i + 1 )st row. The fro04 length h, is defined to be the total numb\_. of points which are either dircctl! to the right or directly betow the (i,j)-point together with the (i, j)-point itself. It wm conjectured by Logan and Shcpp that a tableau is always unique@ determined (up fo reflection} by its set of hook lengths. In this paper, we give several familics of counterexamples to this conjecture. However, by extending the definition of hook length, we show that a tableau is always uniquely determined (up to reflection) by its extended set of hook lengths. * The terminology and definitions folfow that of [ 1, 6).