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To any sequence of real numbers a n n 0 , we can associate another sequence â s s 0 , which Knuth calls its binomial transform. This transform is defined through the rulê a s = B s a n = n (−1) n s n a n . We study the properties of this transform, obtaining rules for its manipulation and a table of transforms, that allow us to invert many transforms by inspection. We use these methods to perform a detailed analysis of skip lists, a probabilistic data structure introduced by Pugh as andoi:10.1016/j.tcs.2005.10.041 fatcat:bgdfjtpedzayjllnbtj4wu7kt4