13 A contribution is made to the classification of lattice-like total perfect 14 codes in integer lattices Λn via pairs (G,Φ) formed by abelian groups G 15 and homomorphisms Φ : Z → G. A conjecture is posed that the cited 16 contribution covers all possible cases. A related conjecture on the unfinished 17 work on open problems on lattice-like perfect dominating sets in Λn with 18 induced compon...

A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G,Φ) formed by abelian groups G and homomorphisms Φ : Z → G. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λn with induced components that are para...

Abstract After collecting a number of results on interval and almost preserving linear maps vector lattice homomorphisms, we show that direct systems in various categories normed lattices Banach have limits, these coincide with limits the naturally associated other categories. For those where general constructions do not work to establish existence describe basic structure exist. A system categ...

We obtain the picture group as the quotient with a torsion subgroup, of an extended picture group, which is isomorphic to the kernel of a precrossed module homomorphism. In addition to expanding the notion of a picture group, the new formulation gives a natural way to construct homomorphisms between picture groups by describing deformations of one-vertex subpictures. The extended picture group ...

In this article, we prove that the height function associated with square-ice model (i.e. six-vertex $$a=b=c=1$$ on square lattice), or, equivalently, of uniform random homomorphisms from $$\mathbb {Z}^2$$ to {Z}$$ , has logarithmic variance. This establishes a strong form roughness function.

As a continuation of [7], we introduce the notions of topological subalgebras, topological ideals and topological homomorphisms in topological BCI-algebras and study some related properties. In the section 3, we investigate the compactness in a TBCI-algebra X and quotient TBCI-algebra X=I where I is a topological ideal of X. In the section 4, we introduce the notion of topological homomorphisms...

Combining the efficient cross-polytope locality-sensitive hash family of Terasawa and Tanaka with the heuristic lattice sieve algorithm of Micciancio and Voulgaris, we show how to obtain heuristic and practical speedups for solving the shortest vector problem (SVP) on both arbitrary and ideal lattices. In both cases, the asymptotic time complexity for solving SVP in dimension n is 2. For any la...

Motivated by the Lipschitz-lifting property of Banach spaces introduced Godefroy and Kalton, we consider lattice-lifting property, which is an analogous notion within category lattices lattice homomorphisms. Namely, a X satisfies if every homomorphism to having bounded linear right-inverse must have right-inverse. In terms free lattices, this can be rephrased into following question: embed they...

A graph homomorphism from a graph G to a graph H is a mapping h : V (G)→ V (H) such that h(u) ∼ h(v) if u ∼ v. Graph homomorphisms are well studied objects and, for suitable choices of eitherG orH, many classical graph properties can be formulated in terms of homomorphisms. For example the question of wether there exists a homomorphism from G to H = Kq is the same as asking wether G is q-colour...