Oron Ze
نویسنده
چکیده
Dyson's conjecture, already proved by Gunson, Wilson and Good, is given a direct com-binatorial proof. We are going to give a combinatorial proof of [Z). The CCVlStUnt term Of n,&i+jcn (1-XJXj)+ iS This conjecture was proved by Gunson [S], Wilson [IO] and Good [5]. Recently Andrews [l] and MacDonald [7] formulated certain generalizations of conjecture which are still open. Andrews conjectured a q-analog, and Ma raised a conjecture on root systems of simple Lie algebras. A related conjecture was raised by Mehta [8] and turned out to follow from a result of Selberg [9] which lay dormant for several decades. [7] also formulated a generalization of Mebta's conjecture for Lie gev and lberg's result to prove this conjecture for all the classical Lie acDonald did the same for Dyson's conjecture. None of the proofs of n's conjecture, of which Good's [5] is particularly elegant, seem to generalize. e believe that our proof has a goo generalized, because most combinatorial proofs involving bin have q-analogs. owever, another i is still neede generalization of e will prove. yson's conjecture in t
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تاریخ انتشار 2001