Sums of lattice homomorphisms
نویسندگان
چکیده
منابع مشابه
Lattice Homomorphisms Induced by Group Homomorphisms
Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...
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 کاملExponentially convergent lattice sums.
For any oblique incidence and arbitrarily high order, lattice sums for one-dimensional gratings can be expressed in terms of exponentially convergent series. The scattering Green's function can be efficiently evaluated also in the grating plane. Numerical implementation of the method is 200 times faster than for the previous best result.
متن کاملLattice Points in Minkowski Sums
Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P .
متن کاملLattice Points, Dedekind Sums, and Ehrhart Polynomials of Lattice Polyhedra
Let σ be a simplex of RN with vertices in the integral lattice ZN . The number of lattice points of mσ (= {mα : α ∈ σ}) is a polynomial function L(σ,m) of m ≥ 0. In this paper we present: (i) a formula for the coefficients of the polynomial L(σ, t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the sequence L(σ,m), m ≥ 0; (...
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: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1992-1086322-8