The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
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∑j=0n(−1)jS(n,j) is nonzero for all n>2. We prove this conjecture for all n≢2 and ≢2944838mod3145728 and discuss applications of this result to graph theory, multiplicative partition functions, and the irrationality of p-adic series.