We show analogues of a theorem due to Valiant and Vazirani [16] for intractable parameterized complexity classes such as W[P], W[SAT] and the classes of the W-hierarchy as well as...
For a fixed polyomial f Z[X], let k(N) denote the maximum size of a set A {1, 2, . . . , N} such that no product of k distinct elements of A is in the value set of f. In this pap...
Sylvester’s identity is a classical determinantal identity with a straightforward linear algebra proof. We present combinatorial proofs of several non-commutative extensions, an...
We use a generalization of Wiener's 1/f theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space W (L , 1 )(Rd ), the corresponding frame operato...
We compare two Picard groups in dimension one. Our proofs are constructive and the results generalize a theorem of J. Sands [11]. MSC 2000: 13C15, 13C20, 03F65, 13F45