A partial lattice P is ideal-projective, with respect to a class C of lattices, if for every K ∈ C and every homomorphism φ of partial lattices from P to the ideal lattice of K, there are arbitrarily large choice functions f : P → K for φ that are also homomorphisms of partial lattices. This extends the traditional concept of (sharp) transferability of a lattice with respect to C. We prove the ...

The lift of K-theoretic D-brane charge to M-theory was recently hypothesized land in Cohomotopy cohomology theory. To further check this "Hypothesis H", here we explicitly compute the constraints on fractional charges at ADE-orientifold singularities imposed by existence lifts from equivariant K-theory theory, through Boardman's comparison homomorphism. We relevant cases and find that condition...

We consider vector lattices endowed with locally solid convergence structures, which are not necessarily topological. show that such a is defined by the to 0 on positive cone. Some results unbounded modification were only available in partial cases generalized. Order characterized as strongest monotone nets converge their extremums (if they exist). partially characterize sublattices order restr...

Graph homomorphisms from the $${\mathbb {Z}}^d$$ lattice to {Z}}$$ are functions on whose gradients equal one in absolute value. These height corresponding proper 3-colorings of and, two dimensions, 6-vertex model (square ice). We consider uniform model, obtained by sampling uniformly such a graph homomorphism subject boundary conditions. Our main result is that delocalizes having no translatio...

We show that certain canonical realizations of the complexes Hom(G,H) and Hom+(G,H) of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For G a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of ...

Rough set theory has a vital role in the mathematical field of knowledge representation problems. Hence, algebraic structure is defined by Pawlak. Mathematics and Computer Science have many applications Lattice. The principle ordered been analyzed logic programming for crypto-protocols. Iwinski extended an approach towards lattice with rough whereas based on depends indiscernibility relation wh...

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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.