30 citations · 75 across the 16 of their papers we have counts for
24 papers
Weighted lattice point enumeration in lecture hall order polytopes
Katharina Jochemko, Krishna Menon
We consider weighted lattice point enumeration in lecture hall order polytopes. We observe that these half-open polytopes are closed under weight-lifting for a large class of polyn…
Ehrhart positivity for marked order polytopes
Katharina Jochemko, Krishna Menon
Given a pair of finite posets , the function counting integer-valued order preserving extensions of an order preserving map from to…
Ehrhart Theory over Abelian Group Rings
Robert Davis, Jesús A. De Loera, Alexey Garber +3
We introduce a unified framework for Ehrhart theory in which lattice point enumerators take coefficients in an Abelian group ring, encoding substantially richer algebraic data than…
How to Learn a Star: Binary Classification with Starshaped Polyhedral Sets
Marie-Charlotte Brandenburg, Katharina Jochemko
We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supp…
On the instability of syzygy bundles on toric surfaces
Lucie Devey, Milena Hering, Katharina Jochemko +1
We show that for every toric surface apart from the projective plane and a product of two projective lines and every ample line bundle there exists a polarisation such that the syz…
Preservation of inequalities under Hadamard products
Petter Brändén, Luis Ferroni, Katharina Jochemko
Wagner (1992) proved that the Hadamard product of two Pólya frequency sequences that are interpolated by polynomials is again a Pólya frequency sequence. We study whether related c…
Polyhedral combinatorics of bisectors
Aryaman Jal, Katharina Jochemko
For any polyhedral norm, the bisector of two points is a polyhedral complex. We study combinatorial aspects of this complex. We investigate the sensitivity of the presence of label…
Weighted Ehrhart Theory: Extending Stanley's nonnegativity theorem
Esme Bajo, Robert Davis, Jesús A. De Loera +4
We generalize R. P. Stanley's celebrated theorem that the -polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under contai…
Lattice zonotopes of degree 2
Matthias Beck, Ellinor Janssen, Katharina Jochemko
The Ehrhart polynomial of a lattice polytope gives the number of integer lattice points in the -th dilate of for all integers . The degree of is…
Learning polytopes with fixed facet directions
Maria Dostert, Katharina Jochemko
We consider the task of reconstructing polytopes with fixed facet directions from finitely many support function evaluations. We show that for a fixed simplicial normal fan the lea…
Ehrhart polynomials of rank two matroids
Luis Ferroni, Katharina Jochemko, Benjamin Schröter
Over a decade ago De Loera, Haws and Köppe conjectured that Ehrhart polynomials of matroid polytopes have only positive coefficients and that the coefficients of the corresponding…
The Eulerian transformation
Petter Brändén, Katharina Jochemko
Eulerian polynomials are fundamental in combinatorics and algebra. In this paper we study the linear transformation defined by $\mat…
Symmetric decompositions and the Veronese construction
Katharina Jochemko
We study rational generating functions of sequences that agree with a polynomial and investigate symmetric decompositions of the numerator polynomial for subseq…
Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity
Katharina Jochemko, Mohan Ravichandran
We characterize all signed Minkowski sums that define generalized permutahedra, extending results of Ardila-Benedetti-Doker (2010). We use this characterization to give a complete…
Linear recursions for integer point transforms
Katharina Jochemko
We consider the integer point transform of a po…
Arithmetic aspects of symmetric edge polytopes
Akihiro Higashitani, Katharina Jochemko, Mateusz Michałek
We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Gröbner ba…
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…
Ehrhart tensor polynomials
Sören Berg, Katharina Jochemko, Laura Silverstein
The notion of Ehrhart tensor polynomials, a natural generalization of the Ehrhart polynomial of a lattice polytope, was recently introduced by Ludwig and Silverstein. We initiate a…
-polynomials of zonotopes
Matthias Beck, Katharina Jochemko, Emily McCullough
The Ehrhart polynomial of a lattice polytope encodes information about the number of integer lattice points in positive integral dilates of . The -polynomial of …
Combinatorial mixed valuations
Katharina Jochemko, Raman Sanyal
Combinatorial mixed valuations associated to translation-invariant valuations on polytopes are introduced. In contrast to the construction of mixed valuations via polarization, com…
On the real-rootedness of the Veronese construction for rational formal power series
Katharina Jochemko
We study real sequences that eventually agree with a polynomial. We show that if the numerator polynomial of its rational generating series is of degr…
Combinatorial positivity of translation-invariant valuations and a discrete Hadwiger theorem
Katharina Jochemko, Raman Sanyal
We introduce the notion of combinatorial positivity of translation-invariant valuations on convex polytopes that extends the nonnegativity of Ehrhart h*-vectors. We give a surprisi…
Order polynomials and Pólya's enumeration theorem
Katharina Jochemko
Pólya's enumeration theorem is concerned with counting labeled sets up to symmetry. Given a finite group acting on a finite set of labeled elements it states that the number of lab…
Arithmetic of marked order polytopes, monotone triangle reciprocity, and partial colorings
Katharina Jochemko, Raman Sanyal
For a poset P, a subposet A, and an order preserving map F from A into the real numbers, the marked order polytope parametrizes the order preserving extensions of F to P. We show t…