Author manuscript, published in "The Ramanujan Journal (2009) 9 pages" Hook lengths and shifted parts of partitions
نویسنده
چکیده
— Some conjectures on partition hook lengths, recently stated by the author, have been proved and generalized by Stanley, who also needed a formula by Andrews, Goulden and Jackson on symmetric functions to complete his derivation. Another identity on symmetric functions can be used instead. The purpose of this note is to prove it.
منابع مشابه
Some Combinatorial Properties of Hook Lengths , Contents , and Parts of Partitions 1 Richard
Citation Stanley, Richard. " Some combinatorial properties of hook lengths, contents, and parts of partitions. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract The main result of this paper is a generalization of a conjecture of Guoniu Han, originally inspired by an identity of Nekrasov and Okounkov. Our result state...
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متن کاملSome Combinatorial Properties of Hook Lengths, Contents, and Parts of Partitions
The main result of this paper is a generalization of a conjecture of Guoniu Han, originally inspired by an identity of Nekrasov and Okounkov. Our result states that if F is any symmetric function (say over Q) and if
متن کاملSome Conjectures and Open Problems on Partition Hook Lengths
Abstract. We present some conjectures and open problems on partition hook lengths, which are all motivated by known results on the subject. The conjectures are suggested by extensive experimental calculations using a computer algebra system. The first conjecture unifies two classical results on the number of standard Young tableaux and the number of pairs of standard Young tableaux of the same ...
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تاریخ انتشار 2009