Federico Ardila ; Federico Castillo ; Jose Samper
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The topology of the external activity complex of a matroid
dmtcs:6355 -
Discrete Mathematics & Theoretical Computer Science,
April 22, 2020,
DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
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https://doi.org/10.46298/dmtcs.6355
The topology of the external activity complex of a matroid
Authors: Federico Ardila 1,2; Federico Castillo 3; Jose Samper 4
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Federico Ardila;Federico Castillo;Jose Samper
1 San Francisco State University
2 Universidad de los Andes [Bogota]
3 University of California [Davis]
4 University of Washington [Seattle]
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.