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The Combinatorics of Differentiation

Bertiger, Anna S. and McEliece, Robert J. and Sweatlock, Sarah (2008) The Combinatorics of Differentiation. In: Sequences and Their Applications - SETA 2008. Lecture Notes in Computer Science. No.5203. Springer , Berlin, pp. 142-152. ISBN 9783540859116.

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Let S_1, S_2, ... be a sequence of finite sets, and suppose we are asked to find the sequence of cardinalities s[1], s[2], .... We are usually satisfied to find a closed-form expression for the a-generating function F_S(z)=∑_(n ≥ 0) s[n]a[n]z^n, where a[n] is a fixed positive causal sequence. But extracting s[n] from F_S (z) is often itself a challenging problem, because of the unnavoidable link to calculus s[n] = (a[n])/(n!)D^n[F(z)]_z = 0. In this paper we will consider the case a[n] = 1/(n!), (exponential generating functions), and find many links between combinatorics and calculus.

Item Type:Book Section
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Additional Information:© Springer-Verlag Berlin Heidelberg 2008.
Series Name:Lecture Notes in Computer Science
Issue or Number:5203
Record Number:CaltechAUTHORS:20180809-133557549
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88704
Deposited By: George Porter
Deposited On:09 Aug 2018 22:05
Last Modified:16 Nov 2021 00:29

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