Outputs (2)

A generalization of a theorem of White (2021)
Journal Article
Batyrev, V., & Hofscheier, J. (2022). A generalization of a theorem of White. Moscow Journal of Combinatorics and Number Theory, 10(4), 281-296. https://doi.org/10.2140/moscow.2021.10.281

An m-dimensional simplex ∆ in Rm is called empty lattice simplex if ∆ ∩ Zm is exactly the set of vertices of ∆. A theorem of White states that if m = 3 then, up to an affine unimodular transformation of the lattice Zm, any empty lattice simplex ∆ ⊂ R... Read More about A generalization of a theorem of White.

Splittings of Toric Ideals (2021)
Journal Article
Favacchio, G., Hofscheier, J., Keiper, G., & Van Tuyl, A. (2021). Splittings of Toric Ideals. Journal of Algebra, 574, 409-433. https://doi.org/10.1016/j.jalgebra.2021.01.012

Let I ⊆ R = K[x1, . . . , xn] be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal I can be “split” into the sum of two smaller toric ideals. For a general toric ideal I, we give a sufficient condition for this splitting in t... Read More about Splittings of Toric Ideals.