TY - JOUR
T1 - Non-Normal Very Ample Polytopes - Constructions and Examples
AU - Lason, Michal
AU - Michalek, Mateusz
PY - 2017
Y1 - 2017
N2 - We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [Cox et al. 14, Question 3.5 (1),(2), Question 3.6], [Beck et al. 15, Conjecture 3.5(a),(b)], and [Hasse et al. 07, Open question 3 (a),(b) p. 2310, Question p. 2316] by constructing a new family of non-normal very ample polytopes. These polytopes are certain segmental fibrations of unimodular graph polytopes, we explicitly compute their invariants - Hilbert function, Ehrhart polynomial, and gap vector.
AB - We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [Cox et al. 14, Question 3.5 (1),(2), Question 3.6], [Beck et al. 15, Conjecture 3.5(a),(b)], and [Hasse et al. 07, Open question 3 (a),(b) p. 2310, Question p. 2316] by constructing a new family of non-normal very ample polytopes. These polytopes are certain segmental fibrations of unimodular graph polytopes, we explicitly compute their invariants - Hilbert function, Ehrhart polynomial, and gap vector.
KW - normal polytope
KW - very ample polytope
KW - graph polytope
KW - Hilbert basis
KW - gap vector
KW - segmental fibration
KW - CONVEX POLYTOPES
KW - TORIC IDEALS
U2 - 10.1080/10586458.2015.1128370
DO - 10.1080/10586458.2015.1128370
M3 - Article
SN - 1058-6458
VL - 26
SP - 130
EP - 137
JO - Experimental Mathematics
JF - Experimental Mathematics
IS - 2
ER -