Counterexamples to the 0-1 conjecture

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dc.creatorMcLarnan, Timothy J.
dc.creatorWarrington, Gregory S.
dc.date2002-09-18
dc.date.accessioned2026-07-07T04:50:57Z
dc.date.available2026-07-07T04:50:57Z
dc.descriptionFor permutations x and w, let mu(x,w) be the coefficient of highest possible degree in the Kazhdan-Lusztig polynomial P_{x,w}. It is well-known that the coefficients mu(x,w) arise as the edge labels of certain graphs encoding the representations of S_n. The 0-1 Conjecture states that the mu(x,w) are either 0 or 1. We present two counterexamples to this conjecture, the first in S_16, for which x and w are in the same left cell, and the second in S_10. The proof of the counterexample in S_16 relies on computer calculations.
dc.description15 pages, 4 figures; code for computer calculations included in source package
dc.identifierhttps://arxiv.org/abs/math/0209221
dc.identifierhttp://arxiv.org/abs/math/0209221
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64980
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject05E15; 20F55
dc.titleCounterexamples to the 0-1 conjecture
dc.typetext

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