Minimal Determinants and Lattice Inequalities
نویسنده
چکیده
Some results of P. McMullen on determinants of sublattices of Z d induced by rational subspaces are generalized to arbitrary lattices. As an application, we obtain an equality for the minimal determinants introduced by J. M. Wills, namely Dt(L) = Dd(L)Dd_((L*). Using an inequality of Lagarias, Lenstra and Schnorr, we generalize two isoperimetric inequalities with lattice constraints by Bokowski, Hadwiger and Wills, and Hadwiger, respectively, to arbitrary lattices.
منابع مشابه
Improved theoretical guarantees regarding a class of two-row cutting planes
The corner polyhedron is described by minimal valid inequalities from maximal lattice-free convex sets. For the Relaxed Corner Polyhedron (RCP) with two free integer variables and any number of non-negative continuous variables, it is known that such facet defining inequalities arise from maximal lattice-free splits, triangles and quadrilaterals. We improve on the tightest known upper bound for...
متن کاملLifting Integer Variables in Minimal Inequalities Corresponding to Lattice-Free Triangles
Recently, Andersen et al. [1] and Borozan and Cornuéjols [3] characterized the minimal inequalities of a system of two rows with two free integer variables and nonnegative continuous variables. These inequalities are either split cuts or intersection cuts derived using maximal lattice-free convex sets. In order to use these minimal inequalities to obtain cuts from two rows of a general simplex ...
متن کاملMILP models and valid inequalities for the two-machine permutation flowshop scheduling problem with minimal time lags
In this paper, we consider the problem of scheduling on two-machine permutation flowshop with minimal time lags between consecutive operations of each job. The aim is to find a feasible schedule that minimizes the total tardiness. This problem is known to be NP-hard in the strong sense. We propose two mixed-integer linear programming (MILP) models and two types of valid inequalities which aim t...
متن کاملIdeal of Lattice homomorphisms corresponding to the products of two arbitrary lattices and the lattice [2]
Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...
متن کاملAdaptive Policies for Reducing Inequalities in the Social Determinants of Health
Inequalities in the social determinants of health (SDH), which drive avoidable health disparities between different individuals or groups, is a major concern for a number of international organisations, including the World Health Organization (WHO). Despite this, the pathways to changing inequalities in the SDH remain elusive. The methodologies and concepts within system science are now viewed ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1992