Codes, transforms and the spectrum of the symmetric group
Paul H. Edelman, Dennis E. White · Pacific Journal of Mathematics · 1990
Let G n be the graph of permutations with edges drawn between permutations differing by an adjacent transposition.Using the Kazhdan-Lusztig representations of S n and combinatorial arguments, we show that integers frequently occur in the spectrum of G n .That 0 and -1 are among the integers which arise has application to finite Radon transforms and to existence of perfect 1-codes on G n .