Geodesic
Sweeping the cd-index and the toric \(h\)-vector
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We derive formulas for the ${\bf cd}$-index and the toric $h$-vector of a convex polytope $P$ from a sweeping by a hyperplane. These arise from interpreting the corresponding $S$-shelling of the dual of $P$. We describe a partition of the faces of the complete truncation of $P$ to reflect explicitly the nonnegativity of its ${\bf cd}$-index and what its components are counting. One corollary is a quick way to compute the toric $h$-vector directly from the ${\bf cd}$-index that turns out to be an immediate consequence of formulas of Bayer and Ehrenborg. We also propose an "extended toric" $h$-vector that fully captures the information in the flag $h$-vector.
DOI : 10.37236/553
Classification : 52B05
Mots-clés : cd-index, toric \(h\)-vector, convex polytope, flag \(h\)-vector 
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     author = {Carl W. Lee},
     title = {Sweeping the cd-index and the toric \(h\)-vector},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/553},
     zbl = {1216.52009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/553/}
}
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Carl W. Lee. Sweeping the cd-index and the toric \(h\)-vector. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/553

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