Given a set X and a set C of subsets of X, subsets of X covered by k sets in C are called k-frequent. Frequent sets are of interest in large scale data analysis, pattern recognition and data mining. Characterization of maximal kfrequent sets in terms of equivalence relation and partial order is given. A general algorithm for finding maximal k-frequent sets, efficient for wide range of practical...

My research in graph theory focuses on asymptotic maximal bounds for Cartesian powers of finite graphs. This line of inquiry was opened up by [4], in which the authors proved that the maximal spherical averaging operator on the N -dimensional hypercube K 2 satisfies a bound in the L 2 norm independent of the dimension N . That is, if Sk(x) := {y : d(x, y) = k} in the graph distance metric on K ...

A graph G = (V, E) is called a split graph if there exists a partition V = I∪K such that the subgraphs G[I] andG[K] of G induced by I andK are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary condition for a split graph G with |I| < |K| to be hamiltonian. We will call a split graph G with |I| < |K| satisfying this condition a Burkard–Hammer graph. Further, a...

We use difference sets to construct interesting sets of lines in complex space. Using (v, k, 1)-difference sets, we obtain k2−k+1 equiangular lines in Ck when k − 1 is a prime power. Using semiregular relative difference sets with parameters (k, n, k, λ) we construct sets of n + 1 mutually unbiased bases in Ck. We show how to construct these difference sets from commutative semifields and that ...

We consider way k tape alternating pushdown automata k apa and way k tape alternating nite automata k afa We say that an alternating automaton accepts a language L with f n bounded maximal respectively minimal leaf size if arbitrary re spectively at least one accepting tree for any w L has no more than f jwj leaves The main results of the article are the following For way k tape alternating cou...

where aij ∈ K. Additive polynomials over valued fields in positive characteristic play an important role in understanding many algebraic and model theoretic properties of maximal fields of positive characteristic, see [7] for a thorough examination of the issue. A subset S of a valued field (K, v) has the optimal approximation property if for all a ∈ K, the set {v(s − a) : s ∈ S} has a maximal ...

The subword complexity of a finite word w of length N is a function which associates to each n ≤ N the number of all distinct subwords of w having the length n. We define the maximal complexity C(w) as the maximum of the subword complexity for n ∈ {1, 2, . . . , N}, and the global maximal complexity K(N) as the maximum of C(w) for all words w of a fixed length N over a finite alphabet. By R(N) ...

A graph is k-degenerate if any induced subgraph has a vertex of degree at most k. In this paper we prove new algorithms finding cliques and similar structures in these graphs. We design linear time Fixed-Parameter Tractable algorithms for induced and non induced bicliques. We prove an algorithm listing all maximal bicliques in time O(k(n−k)2), improving the result of [D. Eppstein, Arboricity an...

It is shown that SBIED(4k 2 , 2Jc 2 ± k, P ± k) and Hadamard matrices with maximal excess exist for qs,q {q:q 1 (mod 4) is a prime power}, + 1, g the length of a Golay sequence}. There a proper n dimensional Hadamard matrix of order (4k2)n. Regular symmetric Hadamard matrices with constant diagonal are obtained for orders 4k2 whenever complete regular 4-sets of regular matrices of order k 2 exist.

Let p be an odd prime number, k an imaginary abelian field containing a primitive p-th root of unity, and k∞/k the cyclotomic Zp-extension. Denote by L/k∞ the maximal unramified pro–p abelian extension, and by L′ the maximal intermediate field of L/k∞ in which all prime divisors of k∞ over p split completely. Let N/k∞ (resp. N ′/k∞) be the pro–p abelian extension generated by all p-power roots ...