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Integrals Don't Have Anything to Do with Discrete Math, Do They?

Year of Award: 2012

Award: Allendoerfer

Publication Information: Mathematics Magazine, vol. 84, 2011, pp. 108-119

Summary: This article is an exposition of some not-so-well known integral formulas for the number of perfect matchings in a graph. Alternating between discrete and continuous topics, the author expresses the number of perfect matchings in a complete bipartite graph in terms of the gamma function. After this initial combination of the discrete and continuous, he expands his collection of improper integrals with the introduction of rook polynomials and derangements.

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About the Author: (From the MathFest 2012 Prizes and Awards Booklet)

Mark Kayll grew up in North Vancouver, British Columbia. After earning mathematics degrees from Simon Fraser University (B.Sc. 1987) and Rutgers University (Ph.D. 1994), he joined the faculty at the University of Montana in Missoula. He's enjoyed sabbaticals in Slovenia (University of Ljubljana, 2001–02) and Canada (Université de Montréal, 2008–09).

His publications fall in the discrete realm and have touched on combinatorics, graph theory, number theory, and probability. Mark's musical interests, such as playing the banjo, have motivated him in recent years to develop a general education course on mathematics and music for non-math majors.

He lives in Missoula with his wife, Jennifer (an excellent editor), and two beautiful children, Samuel and Leah.

MSC Codes: 
26Axx, 05Cxx
Author(s): 
P. Mark Kayll
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Publication Date: 
Tuesday, August 7, 2012
Publish Page: 
Summary: 

An exposition of some not-so-well known integral formulas for the number of perfect matchings in a graph. Alternating between discrete and continuous topics, the author expresses the number of perfect matchings in a complete bipartite graph in terms of the gamma function. After this initial combination of the discrete and continuous, he expands his collection of improper integrals with the introduction of rook polynomials and derangements.

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