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Summary
Calculus and combinatorics overlap, in that power series can be used to study combinatorially defined sequences. In this paper, we use exponential generating functions to study a curious refinement of the Euler numbers, which count the number of “up-down” permutations of length n.
Additional information
Notes on contributors
Fiacha Heneghan
Fiacha Heneghan ([email protected]) is a senior at DePaul University, double-majoring in mathematical sciences and philosophy. His mathematical interests incline toward combinatorics and algebra, while his non-mathematical ones include blues guitar, sword fighting, and bird-watching.
Kyle Petersen
Kyle Petersen ([email protected]) earned an A.B. in mathematics from Washington University in St. Louis in 2001 and a Ph.D. in mathematics from Brandeis University in 2006. After a wonderful three years at the University of Michigan, he joined the faculty at DePaul University, where he is now an associate professor. His research is in algebraic, enumerative, and topological combinatorics. Outside of the math department, he enjoys running, cooking, and spending time with his wife and their three children.