Facets of the r-stable (n, k)-hypersimplex

T. Hibi, L.T. Solus, Annals of Combinatorics 20 (2016) 815–829.

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Journal Article | Published
Author
Hibi, Takayugi; Solus, Liam TIST Austria
Abstract
Let k, n, and r be positive integers with k < n and r≤⌊nk⌋. We determine the facets of the r-stable n, k-hypersimplex. As a result, it turns out that the r-stable n, k-hypersimplex has exactly 2n facets for every r<⌊nk⌋. We then utilize the equations of the facets to study when the r-stable hypersimplex is Gorenstein. For every k > 0 we identify an infinite collection of Gorenstein r-stable hypersimplices, consequently expanding the collection of r-stable hypersimplices known to have unimodal Ehrhart δ-vectors.
Publishing Year
Date Published
2016-12-01
Journal Title
Annals of Combinatorics
Acknowledgement
Liam Solus was supported by a 2014 National Science Foundation/Japan Society for the Promotion of Science East Asia and Pacific Summer Institute Fellowship. Open access funding provided by IST Austria.
Volume
20
Issue
4
Page
815 - 829
IST-REx-ID

Cite this

Hibi T, Solus LT. Facets of the r-stable (n, k)-hypersimplex. Annals of Combinatorics. 2016;20(4):815-829. doi:10.1007/s00026-016-0325-x
Hibi, T., & Solus, L. T. (2016). Facets of the r-stable (n, k)-hypersimplex. Annals of Combinatorics, 20(4), 815–829. https://doi.org/10.1007/s00026-016-0325-x
Hibi, Takayugi, and Liam T Solus. “Facets of the R-Stable (n, k)-Hypersimplex.” Annals of Combinatorics 20, no. 4 (2016): 815–29. https://doi.org/10.1007/s00026-016-0325-x.
T. Hibi and L. T. Solus, “Facets of the r-stable (n, k)-hypersimplex,” Annals of Combinatorics, vol. 20, no. 4, pp. 815–829, 2016.
Hibi T, Solus LT. 2016. Facets of the r-stable (n, k)-hypersimplex. Annals of Combinatorics. 20(4), 815–829.
Hibi, Takayugi, and Liam T. Solus. “Facets of the R-Stable (n, k)-Hypersimplex.” Annals of Combinatorics, vol. 20, no. 4, Springer, 2016, pp. 815–29, doi:10.1007/s00026-016-0325-x.

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