By Dennis Stanton

The notes that at last turned this publication have been written among 1977 and 1985 for the path known as positive Combinatorics on the college of Minnesota. this can be a one-quarter (10 week) path for top point undergraduate scholars. the category often includes arithmetic and desktop technology majors, with an occasional engineering scholar. a number of graduate scholars in computing device technology additionally attend. At Minnesota, optimistic Combinatorics is the 3rd sector of a 3 area series. the 1st area, Enumerative Combinatorics, is on the point of the texts via Bogart [Bo], Brualdi [Br], Liu [Li] or Tucker [Tu] and is a prerequisite for this path. the second one region, Graph thought and Optimization, isn't really a prerequisite. We think that the scholars are conversant in the options of enumeration: easy counting rules, producing capabilities and inclusion/exclusion. This direction advanced from a path on combinatorial algorithms. That direction contained a mix of graph algorithms, optimization and directory algorithms. the pc assignments normally consisted of trying out algorithms on examples. whereas we felt that such fabric used to be worthwhile and never with no mathematical content material, we didn't imagine that the path had a coherent mathematical concentration. moreover, a lot of it used to be being taught, or might have been taught, in other places. Graph algorithms and optimization, for example, have been inserted into the graph concept path the place they certainly belonged. the pc technology division already taught a number of the fabric: the better algorithms in a discrete arithmetic path; potency of algorithms in a extra complex path.