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dc.creatorWilliams, Lauren
dc.date2009-02-20T07:35:02Z
dc.date2005
dc.date.accessioned2012-06-07T21:54:31Z
dc.date.available2012-06-07T21:54:31Z
dc.date.issued2012-06-07
dc.identifierWilliams, Lauren K. 2005. Enumeration of totally positive Grassmann cells. Advances in Mathematics 190(2): 319-342.
dc.identifier0001-8708
dc.identifierhttp://nrs.harvard.edu/urn-3:HUL.InstRepos:2624454
dc.identifier.urihttps://repositorio.leon.uia.mx/xmlui/123456789/33198
dc.descriptionPostnikov (Webs in totally positive Grassmann cells, in preparation) has given a combinatorially explicit cell decomposition of the totally nonnegative part of a Grassmannian, denoted \(Gr_{kn ^+}\) and showed that this set of cells is isomorphic as a graded poset to many other interesting graded posets. The main result of our work is an explicit generating function which enumerates the cells in \(Gr_{kn ^+}\) according to their dimension. As a corollary, we give a new proof that the Euler characteristic of \(Gr_{kn ^+}\) is 1. Additionally, we use our result to produce a new \(q\)-analog of the Eulerian numbers, which interpolates between the Eulerian numbers, the Narayana numbers, and the binomial coefficients.
dc.descriptionMathematics
dc.languageen_US
dc.publisherElsevier Science B.V. Amsterdam
dc.relationhttp://dx.doi.org/10.1016/j.aim.2004.01.003
dc.relationhttp://arxiv.org/pdf/math/0307271v1
dc.relationhttp://www.math.harvard.edu/~lauren/TNNsubmit.ps
dc.relationAdvances in Mathematics
dc.subjectGrassmannian
dc.subjectQ-analogs
dc.subjectEulerian numbers
dc.subjecttotal positivity
dc.titleEnumeration of Totally Positive Grassmann Cells


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