Let G be a t uniform s regular linear hypergraph with r vertices It is shown that the number of independent sets I G in G satis es log I G r t O log ts s This leads to an improvement of a previous bound by Alon obtained for t i e for regular ordinary graphs It is also shown that for the Hamming graph H n q with vertices consisting of all n tuples over an alphabet of size q and edges connecting ...

A non-empty set X of a carrier A of an algebra A is called Q-independent if the equality of two term functions f and g of the algebra A on any finite system of elements a1, a2, . . . , an of X implies f(p(a1), p(a2), . . . , p(an)) = g(p(a1), p(a2), . . . , p(an)) for any mapping p ∈ Q. An algebra B is a retract of A if B is the image of a retraction (i.e. of an idempotent endomorphism of B). W...

Large datasets introduce challenges to the scalability of query answering. Given a query Q and a dataset D, it is often prohibitively costly to compute the query answers Q(D) when D is big. To this end, one may want to use heuristics, “quick and dirty” algorithms which return approximate answers. However, in many applications it is a must to find exact query answers. So, how can we efficiently ...

Abstract We show that independent and uniformly distributed sampling points are asymptotically as good optimal for the approximation of functions from Sobolev spaces $W_p^s(\varOmega )$ on bounded convex domains $\varOmega \subset{\mathbb{R}}^d$ in $L_q$-norm if $q<p$. More generally, we characterize quality arbitrary point sets $P\subset \varOmega $ via $L_\gamma (\varOmega )$-norm dist...

In this paper, we classify the regular embeddings of arc-transitive simple graphs of order pq for any two primes p and q (not necessarily distinct) into orientable surfaces. Our classification is obtained by direct analysis of the structure of arc-regular subgroups (with cyclic vertex-stabilizers) of the automorphism groups of such graphs. This work is independent of the classification of primi...

Let φ : R → R be a continuously differentiable function on an interval J ⊂ R and let α = (α1, α2) be a point with algebraically conjugate coordinates such that the minimal polynomial P of α1, α2 is of degree ≤ n and height ≤ Q. Denote by Mn φ (Q, γ, J) the set of such points α such that |φ(α1)− α2| ≤ c1Q −γ . We show that for a real 0 < γ < 1 and any sufficiently large Q there exist positive va...

Abstract. For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0, let K−s 2 (p, q) denote the set of 2−connected bipartite graphs which can be obtained from Kp,q by deleting a set of s edges. In this paper, we prove that for any graph G ∈ K−s 2 (p, q) with p ≥ q ≥ 3 and 1 ≤ s ≤ q−1, if the number of 3-independent partitions of G is 2p−1 + 2q−1 + s + 4, then G is chromatically unique. This result extends...