The Rise and Fall of the dot com Entrepreneurs

This paper looks at the dot com phenomenon drawing mainly on examples from the USA where the boom started and was most pronounced, but also from the UK which had a number of high profile dot coms. It starts by asking the question, ‘Who were the dot coms?’. it then goes on to consider the factors which led to the emergence of the dot coms such as the emergence of the commercial Internet, the lowering of entry barriers which followed from this and the funding available for new businesses through venture capital. The article also looks at the reasons why it was believed that the dot coms represented a threat to established businesses. The article then looks at the booming IPO market for dot coms and the opportunities this provided for exit by venture capital investors. The crash of 2000 is considered, lessons are drawn for entrepreneurs and investors and finally the article will look at future prospects for the dot com sector

On a conjecture of Wilf

Let n and k be natural numbers and let S(n,k) denote the Stirling numbers of the second kind. It is a conjecture of Wilf that the alternating sum \sum_{j=0}^{n} (-1)^{j} S(n,j) is nonzero for all n>2. We prove this conjecture for all n not congruent to 2 and not congruent to 2944838 modulo 3145728 and discuss applications of this result to graph theory, multiplicative partition functions, and the irrationality of p-adic series.Comment: 18 pages, final version, accepted for publication in the Journal of Combinatorial Theory, Series