66 citations · 448 across the 34 of their papers we have counts for
3 papers · 1 filter
On the irreducibility of a truncated binomial expansion
Michael Filaseta, Angel Kumchev, Dmitrii V. Pasechnik
Let P_nk(x) denote the sum of the lowest k+1 terms in the expansion of (1+x)^n. We investigate the irreducibility of P_nk(x) and more general univariate polynomials related to it.…
Improved bounds for the crossing numbers of K_m,n and K_n
E. de Klerk, J. Maharry, D. V. Pasechnik +2
It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)…
Polynomial-time computing over quadratic maps I: sampling in real algebraic sets
Dima Grigoriev, Dmitrii V. Pasechnik
Given a quadratic map Q : K^n -> K^k defined over a computable subring D of a real closed field K, and a polynomial p(Y_1,...,Y_k) of degree d, we consider the zero set Z=Z(p(Q(X))…