Show simple item record

dc.contributor.authorBlanco Rodriguez, Saulen_US
dc.date.accessioned2012-06-28T20:57:33Z
dc.date.available2017-06-01T06:00:32Z
dc.date.issued2012-01-31en_US
dc.identifier.otherbibid: 7745389
dc.identifier.urihttps://hdl.handle.net/1813/29476
dc.description.abstractLet (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.isoen_USen_US
dc.subjectCoxeter groupen_US
dc.subjectBruhat graphen_US
dc.subjectcomplete cd-indexen_US
dc.titleShortest Path Poset Of Bruhat Intervals And The Complete Cd-Indexen_US
dc.typedissertation or thesisen_US
thesis.degree.disciplineMathematics
thesis.degree.grantorCornell Universityen_US
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh. D., Mathematics
dc.contributor.chairBillera, Louis J.en_US
dc.contributor.committeeMemberTardos, Evaen_US
dc.contributor.committeeMemberSwartz, Edward B.en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Statistics