An Alternate Approach to Alternating Sums: A Method to DIE For

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow
Jennifer J. Quinn, University of Washington TacomaFollow

Publication Date

5-1-2008

Document Type

Article

Abstract

Positive sums count. Alternating sums match. Alternating sums of binomial coefficients, Fibonacci numbers, and other combinatorial quantities are analyzed using sign-reversing involutions. In particular, we Describe the quantity being considered, match positive and negative terms through an Involution, and count the Exceptions to the matching rule (the method of D.I.E.). Careful use of this technique often results in nice generalizations. Any sum arising from the Principle of Inclusion-Exclusion (P.I.E.), such as the number of derangements, can be understood using D.I.E. too.

Publication Title

College Mathematics Journal

Volume

39

Issue

3

First Page

191

Last Page

202

Publisher Policy

post-print

Recommended Citation

Benjamin, Arthur T. and Quinn, Jennifer J., "An Alternate Approach to Alternating Sums: A Method to DIE For" (2008). SIAS Faculty Publications. 213.
https://digitalcommons.tacoma.uw.edu/ias_pub/213