Publications

Please submit all program related publications via this form.

Please acknowledge the support of the SPP in your publications with one of the following phrases:

[...] was supported by the SPP 2458 "Combinatorial Synergies", funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number(s)

or simply

funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number(s)

If multiple projects are involved in your publication, list all of the relevant project numbers, separated by commas.

04/03/2025
The Likelihood Correspondence [ preprint ]
by Thomas Kahle, Hal Schenck, Bernd Sturmfels, Maximilian Wiesmann

An arrangement of hypersurfaces in projective space is SNC if and only if its Euler discriminant is nonzero. We study the critical loci of all Laurent monomials in the equations of the smooth hypersurfaces. These loci form an irreducible variety in the product of two projective spaces, known in algebraic statistics as the likelihood correspondence and in particle physics as the scattering correspondence. We establish an explicit determinantal representation for the bihomogeneous prime ideal of this variety.

05/11/2024
Lattice supported distributions and graphical models [ preprint ]
by Thomas Kahle, Seth Sullivant

For the distributions of finitely many binary random variables, we study the interaction of restrictions of the supports with conditional independence constraints. We prove a generalization of the Hammersley-Clifford theorem for distributions whose support is a natural distributive lattice: that is, any distribution which has natural lattice support and satisfies the pairwise Markov statements of a graph must factor according to the graph. We also show a connection to the Hibi ideals of lattices. dui fames leo sodales risus, posuere justo curae nostra, luctus vitae montes potenti, lectus sem.

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