All the posets/lattices considered here are finite with element 0. An element x of a poset satisfying certain properties is deletable if P − x is a poset satisfying the same properties. A class of posets is reducible if each poset of this class admits at least one deletable element. When restricted to lattices, a class of lattices is reducible if and only if one can go from any lattice in this ...

We obtain several results that distinguish self-reducibility of a language L with the question of whether search reduces to decision for L. These include: (i) If NE 6 = E, then there exists a set L in NP ? P such that search reduces to decision for L, search does not nonadaptively reduces to decision for L, and L is not self-reducible. 1 (ii) If UE 6 = E, then there exists a language L 2 UP ? P...

Abstract The equivariant Heegaard genus of a 3-manifold W with the action finite group G diffeomorphisms is smallest an splitting for . Although reducible manifold and although if reducible, there essential sphere, we show that may be super-additive, additive, or sub-additive under connected sum. Using thin position theory 3-dimensional orbifolds, establish sharp bounds on manifolds, similar to...

We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the ring Z[[x]] of formal power series with integer coefficients. For n,m ≥ 1 and p prime, we show that p+pβx+αx is reducible in Z[[x]] if and only if it is reducible in Zp[x], the ring of polynomials over the p-adic integers.

The main result of this paper is the following: Any language in ESPACE that is bounded truthtable reducible in polynomial time to a set with very high space-bounded Kolmogorov complexity must be bounded truth-table reducible in polynomial time to a sparse set.

We construct a minimal rK-degree, continuum many, in fact. We also show that every minimal sequence, that is, a sequence with minimal rK-degree, must have very low descriptional complexity, that every minimal sequence is rK-reducible to a random sequence, and that there is a random sequence with no minimal sequence rK-reducible to it.

The variety C(3, n) of commuting triples of n × n matrices over C is shown to be irreducible for n = 7. It had been proved that C(3, n) is reducible for n ≥ 30, but irreducible for n ≤ 6. Guralnick and Omladič have conjectured that it is reducible for n > 7.

Let |Λ| 6= Y be arbitrary. Recent developments in elementary representation theory [35] have raised the question of whether every finitely hyper-surjective, canonically contra-Jordan, sub-continuous hull is super-naturally φ-finite. We show that Θ is not greater than x̃. This reduces the results of [35] to an easy exercise. In [35], the authors address the degeneracy of quasi-Fréchet, holomorphi...

We show how to compute the number of reducible cubic scrolls of codimension 2 in Pn incident to the appropriate number of linear spaces.

In the paper two notions related to local (distributed) computations are identified and discussed. The first one is the notion of reducible graphs. A graph is reducible if it can be reduced to a singleton by successive removing its removable nodes; to decide whether a node is removable or not it is sufficient to inspect its neighborhood, hence the removing procedure is local. The second is the ...