Geodesic
Flip posets of Bruhat intervals
Saúl A. Blanco1
1Indiana University
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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In this paper we introduce a way of partitioning the paths of shortest lengths in the Bruhat graph $B(u,v)$ of a Bruhat interval $[u,v]$ into rank posets $P_{i}$ in a way that each $P_{i}$ has a unique maximal chain that is rising under a reflection order. In the case where each $P_{i}$ has rank three, the construction yields a combinatorial description of some terms of the complete $\textbf{cd}$-index as a sum of ordinary $\textbf{cd}$-indices of Eulerian posets obtained from each of the $P_{i}$.
DOI : 10.37236/7910
Classification : 20F55, 05E16
Mots-clés : Bruhat interval, complete cd-index, partitioning of paths of shortest lengths, Bruhat graph, rank posets

Saúl A. Blanco  1

1 Indiana University 
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     author = {Sa\'ul A. Blanco},
     title = {Flip posets of {Bruhat} intervals},
     journal = {The electronic journal of combinatorics},
     year = {2018},
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     number = {4},
     doi = {10.37236/7910},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/7910/}
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Saúl A. Blanco. Flip posets of Bruhat intervals. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7910

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