Publisher's Synopsis
Excerpt from On the Two-Dimensional Davenport Schinzel Problem
We analyze the combinatorial complexity of the minimum M (x, y) of n continuous bivariate functions satisfying the conditions: (a) Each triple of functions intersect in at most s points. (b) Each pair of functions intersect in a curve having at most t singular points. (0) Each of the curves in (b) intersects every plane x const in at most two points. We show that under these assumptions the complexity of M is at most where the constant of proportionality depends on s and t, and where M(q) is an almost linear function of q yielding the maximal number of connected graph portions composing the minimum of q univariate continuous functions, each pair of which intersect in at most r points. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
