Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Castillo Federico

Tuesday 5
Eric Fusy
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
The topology of the external activity complex of a matroid
Federico Ardila  1, 2  , Federico Castillo  3  , Jose Samper  4  
1 : San Francisco State University  (SFSU)
1600 Holloway AveSan FranciscoCA 94132 -  États-Unis
2 : Universidad de los Andes [Bogota]  -  Website
3 : University of California [Davis]  (UC Davis)  -  Website
One Shields Avenue, Davis, CA 95616-5294 -  États-Unis
4 : University of Washington [Seattle]  -  Website
Seattle, Washington 98105 -  États-Unis

We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of Las Vergnas's external/internal order <ext/int on M provides a shelling of Act<(M). We also show that every linear extension of Las Vergnas's internal order <int on M provides a shelling of the independence complex IN(M). As a corollary, Act<(M) and M have the same h-vector. We prove that, after removing its cone points, the external activity complex is contractible if M contains U3,1 as a minor, and a sphere otherwise. 

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