IJPAM: Volume 17, No. 2 (2004)

ORDER REGULARITY FOR BIRKHOFF
INTERPOLATION PROBLEMS OVER $GF(p)$

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Fix integers $n > 0$, $m > 0$ and $M>0$ such that $m \le 2M+1$ and a prime $p > (M/2)^{n+1} (n+2)^{(n+2)/2}$. Let $E$ be a Birkhoff matrix of type $(n,m)$ whose associated Birkhoff problem is order regular. Here we prove that for all $m$-ples $x_i$, $1 \le i \le m$, of integers such that $-M \le x_1 < \cdots < x_m \le M$ the Birkhoff problem associated to $E$ for the field $GF(p)$ is regular at the $m$-ple $(P_1,\dots ,P_m)$, where $P_i\in GF(p)$ is the reduction modulo $p$ of $x_i$.

Received: July 28, 2004

AMS Subject Classification: 41A05, 12E20

Key Words and Phrases: Birkhoff interpolation problem, order regularity of a Birkhoff interpolation problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 17
Issue: 2