Transfer-matrix methods meet Ehrhart theory
نویسندگان
چکیده
منابع مشابه
Weighted Ehrhart Theory and Orbifold Cohomology
We introduce the notion of a weighted δ-vector of a lattice polytope. Although the definition is motivated by motivic integration, we study weighted δ-vectors from a combinatorial perspective. We present a version of Ehrhart Reciprocity and prove a change of variables formula. We deduce a new geometric interpretation of the coefficients of the Ehrhart δ-vector. More specifically, they are sums ...
متن کاملPreserving Privacy and Fidelity via Ehrhart Theory∗
Differential Privacy (DP) has emerged as a sound mathematical framework to quantify vulnerability of algorithms to privacy breaches. Assessing information leakage when databases are subject to unlimited querying is critical. In this work, we consider the noninteractive scenario wherein a sanitized database is extracted via a DP mechanism, on which all further querying is performed. The central ...
متن کاملContributions to the Theory of Ehrhart Polynomials
In this thesis, we study the Ehrhart polynomials of different polytopes. In the 1960's Eugene Ehrhart discovered that for any rational d-polytope P, the number of lattice points, i(P,m), in the mth dilated polytope mP is always a quasi-polynomial of degree d in m, whose period divides the least common multiple of the denominators of the coordinates of the vertices of P. In particular, if P is a...
متن کاملKneser’s Theorem and Inequalities in Ehrhart Theory
We demonstrate how additive number theory can be used to produce new classes of inequalities in Ehrhart theory. More specifically, we use a classical result of Kneser to produce new inequalities between the coefficients of the Ehrhart δ-vector of a lattice polytope. The inequalities are indexed by the vertices of rational polyhedra Q(r, s) ⊆ R for 0 ≤ r ≤ s. As an application, we deduce all pos...
متن کاملMethods of algebraic geometry in matrix theory
The purpose of these lectures to report on the recent solution of a 50 years old problem of describing the set of the eigenvalues of a sum of two hermitian matrices with prescribed eigenvalues 1 Statement of the problem For a field F denote by F the vector space of column vectors f = (f1, ..., fn) with entries in F. We will mostly assume that F is either the field of reals R or complexes C. We ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.03.004