dc.contributor.author Blanco Rodriguez, Saul en_US dc.date.accessioned 2012-06-28T20:57:33Z dc.date.available 2017-06-01T06:00:32Z dc.date.issued 2012-01-31 en_US dc.identifier.other bibid: 7745389 dc.identifier.uri https://hdl.handle.net/1813/29476 dc.description.abstract Let (W, S ) be a Coxeter system, [u, v ] be a Bruhat interval and B (u, v ) be its corresponding Bruhat graph. The combinatorial and topological structures of the longest u-v paths of B (u, v ) have been studied extensively and is well-known. Nevertheless, not much is known of the remaining paths. Here we define the shortest path poset of [u, v ], denoted by SP (u, v ), which arises from the shortest u-v paths of B (u, v ). If W is finite, then SP (e, w0 ) is the union of Boolean posets, where w0 is the longest-length word of W . Furthermore, if SP (u, v ) has a unique rising chain under a reflection order, then SP (u, v ) is EL-shellable. The complete cd-index of a Bruhat interval is a non-homogeneous polynomial that encodes the descent-set distribution, under a reflection order, of paths of B (u, v ). The highest-degree terms of the complete cd-index correspond to the cd-index of [u, v ] (as an Eulerian poset). We study properties of the complete cd-index and compute it for some intervals utilizing an extension of the CL¨ labeling of Bjorner and Wachs that can be defined for dihedral intervals (which we characterize by their complete cd-index) and intervals in a universal Coxeter system. We also describe the lowest-degree terms of the complete cd-index for some intervals. en_US dc.language.iso en_US en_US dc.subject Coxeter group en_US dc.subject Bruhat graph en_US dc.subject complete cd-index en_US dc.title Shortest Path Poset Of Bruhat Intervals And The Complete Cd-Index en_US dc.type dissertation or thesis en_US thesis.degree.discipline Mathematics thesis.degree.grantor Cornell University en_US thesis.degree.level Doctor of Philosophy thesis.degree.name Ph. D., Mathematics dc.contributor.chair Billera, Louis J. en_US dc.contributor.committeeMember Tardos, Eva en_US dc.contributor.committeeMember Swartz, Edward B. en_US
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