Geodesic
Shellability of posets of labeled partitions and arrangements defined by root systems
Emanuele Delucchi1 ; Noriane Girard1 ; Giovanni Paolini2
1Université de Fribourg
2Scuola Normale Superiore, Pisa
The electronic journal of combinatorics, Tome 26 (2019) no. 4
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We prove that the posets of connected components of intersections of toric and elliptic arrangements defined by root systems are EL-shellable and we compute their homotopy type. Our method rests on Bibby's description of such posets by means of "labeled partitions": after giving an EL-labeling and counting homology chains for general posets of labeled partitions, we obtain the stated results by considering the appropriate subposets.
DOI : 10.37236/7160
Classification : 05E45, 06A07, 52B22, 52C35, 05E18
Mots-clés : hyperplane arrangement, toric arrangement, elliptic arrangement, Weyl group, representation stability

Emanuele Delucchi  1   ; Noriane Girard  1   ; Giovanni Paolini  2

1 Université de Fribourg
2 Scuola Normale Superiore, Pisa 
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     title = {Shellability of posets of labeled partitions and arrangements defined by root systems},
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Emanuele Delucchi; Noriane Girard; Giovanni Paolini. Shellability of posets of labeled partitions and arrangements defined by root systems. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/7160

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