3 citations · 4 across the 7 of their papers we have counts for
9 papers
Graded Cohen-Macaulay domains and lattice polytopes with short -vector
Lukas Katthän, Kohji Yanagawa
Let P be a lattice polytope with -vector . In this note we show that if , then is IDP. More generally, we show the corresponding state…
A unified framework of SAGE and SONC polynomials and its duality theory
Lukas Katthän, Helen Naumann, Thorsten Theobald
We introduce and study a cone which consists of a class of generalized polynomial functions and which provides a common framework for recent non-negativity certificates of polynomi…
Smooth centrally symmetric polytopes in dimension 3 are IDP
Matthias Beck, Christian Haase, Akihiro Higashitani +4
In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda's conjecture for centrally symmetric -dimensional polytopes, by s…
When is a polynomial ideal binomial after an ambient automorphism?
Lukas Katthän, Mateusz Michałek, Ezra Miller
Can an ideal I in a polynomial ring k[x] over a field be moved by a change of coordinates into a position where it is generated by binomials with c in k, or by unital…
Finding binomials in polynomial ideals
Anders Jensen, Thomas Kahle, Lukas Katthän
We describe an algorithm which finds binomials in a given ideal and in particular decides whether binomials exist in at all. Binomials in po…
Algebraic properties of ideals of poset homomorphisms
Martina Juhnke-Kubitzke, Lukas Katthän, Sara Saeedi Madani
Given finite posets and , we consider a specific ideal , whose minimal monomial generators correspond to order-preserving maps . We study algebraic…