Let Gn,k denote the Kneser graph whose vertices are the n-element subsets of a (2n + k)-element set and whose edges are the disjoint pairs. In this paper we prove that for any non-negative integer s there is no graph homomorphism from G4,2 to G4s+1,2s+1. This confirms a conjecture of Stahl in a special case.

We study the logarithmic superconformal field theories. Explicitly, the two–point functions of N = 1 logarithmic superconformal field theories (LSCFT) when the Jordan blocks are two (or more) dimensional, and when there are one (or more) Jordan block(s) have been obtained. Using the well known three-point fuctions of N = 1 superconformal field theory (SCFT), three–point functions of N = 1 LSCFT...

Finite State Machine (FSM) model is widely used in the construction of binary convolutional codes. If Z2 = {0, 1} is the binary mod-2 addition group and Z n 2 is the n-times direct product of Z2, then a binary convolutional encoder, with rate k n < 1 and memory m, is a FSM with Z2 as inputs group, Z n 2 as outputs group and Z m 2 as states group. The next state mapping ν : Z2⊕Z m 2 → Z m 2 is a...

Proof. The intersection P of all subfields of F is a field by Exercise 1.4. Consider the ring homomorphism φ : Z → F given by φ(n) = n · 1. Since any subfield contains 1 and is closed under addition, imφ is contained in P . If Char F = p 6= 0 then imφ is isomorphic to Z/pZ = Fp. Since this is a field, we have P = imφ ∼= Fp. If Char F = 0 then φ is injective. Define φ̂ : Q → F by φ̂(m/n) = φ(m)/φ(...

We describe all degenerations of the variety $\mathfrak{Jord}_3$ Jordan algebras dimension three over $\mathbb{C}.$ In particular, we irreducible components in $\mathfrak{Jord}_3.$ For every $n$ define an $n$-dimensional rigid ''marginal'' algebra level one. Also, discuss associative, alternative, left non-commutative Jordan, Leibniz, and anticommutative cases.

A graph G is a homomorphic preimage of another graph H, or equivalently G is H-colorable, if there exists a graph homomorphism f : G → H. A classic problem is to characterize the family of homomorphic preimages of a given graph H. A geometric graph G is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position A geometric homomorphism (resp. ...

We show that for every sofic chunk $E$ there is a bijective homomorphism $f: E_c \rightarrow E$, where $E_c$ of the group computable permutations $\mathbb{N}$ so approximating morphisms can be viewed as restrictions to finite subsets $\mathbb{N}$. Using this we study some relevant effectivity conditions associated with chunks and their profiles.

We study the logarithmic superconformal field theories. Explicitly, the two–point functions of N = 1 logarithmic superconformal field theories (LSCFT) when the Jordan blocks are two (or more) dimensional, and when there are one (or more) Jordan block(s) have been obtained. Using the well known three-point fuctions of N = 1 superconformal field theory (SCFT), three–point functions of N = 1 LSCFT...

We consider four different models of process interactions that unify and generalise models introduced and studied by Angluin et al. [AAD04] and models introduced and studied by Mazurkiewicz [Maz04a,Maz04b]. We encode these models by labelled (hyper)graphs and relabelling rules on this labelled (hyper)graphs called negotiations. Then for these models, we give complete characterisations of labell...