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.
https://resolver.caltech.edu/CaltechAUTHORS:20180809-133557549

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## Abstract

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 | ||||||

DOI: | 10.1007/978-3-540-85912-3_13 | ||||||

Record Number: | CaltechAUTHORS:20180809-133557549 | ||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180809-133557549 | ||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||

ID Code: | 88704 | ||||||

Collection: | CaltechAUTHORS | ||||||

Deposited By: | George Porter | ||||||

Deposited On: | 09 Aug 2018 22:05 | ||||||

Last Modified: | 16 Nov 2021 00:29 |

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