Cet article introduit les gamma-triangles, qui sont liés aux F-triangles et H-triangles utilisés dans l’étude combinatoire des complexes d’amas, et dont ils sont en quelque sorte une version plus fondamentale. On démontre que les gamma-triangles s’expriment comme des sommes de gamma-vecteurs locaux, introduits par Athanasiadis comme un raffinement des h-vecteurs locaux de subdivisions simpliciales, dûs à Stanley. On calcule ensuite explicitement les gamma-triangles des complexes d’amas de type fini.
This article introduces Gamma-triangles, which are closely related to F-triangles and H-triangles that were used in the combinatorial study of cluster complexes, and in some sense are more fundamental. We prove that Gamma-triangles can be expressed as sums of local gamma-vectors, that were introduced by Athanasiadis as a refinement of the Stanley’s local h-vector of simplicial subdivisions. We compute explicitly the Gamma-triangles for cluster complexes of finite type.
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Frédéric Chapoton 1
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@article{AFST_2020_6_29_4_907_0,
author = {Fr\'ed\'eric Chapoton},
title = {A note on gamma triangles and local gamma vectors (with an appendix by {Alin} {Bostan)}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {907--925},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 29},
number = {4},
year = {2020},
doi = {10.5802/afst.1649},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1649/}
}
TY - JOUR AU - Frédéric Chapoton TI - A note on gamma triangles and local gamma vectors (with an appendix by Alin Bostan) JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 907 EP - 925 VL - 29 IS - 4 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1649/ DO - 10.5802/afst.1649 LA - en ID - AFST_2020_6_29_4_907_0 ER -
%0 Journal Article %A Frédéric Chapoton %T A note on gamma triangles and local gamma vectors (with an appendix by Alin Bostan) %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 907-925 %V 29 %N 4 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1649/ %R 10.5802/afst.1649 %G en %F AFST_2020_6_29_4_907_0
Frédéric Chapoton. A note on gamma triangles and local gamma vectors (with an appendix by Alin Bostan). Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 4, pp. 907-925. doi : 10.5802/afst.1649. https://afst.centre-mersenne.org/articles/10.5802/afst.1649/
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