Selected Preprints

1. Here are the slides (Examples-Friends or Foes Part I and Examples-Friends or Foes Part II) for the talk, Examples–Friends or Foes that’s upcoming for January 31, 2017. While, the slides themselves are insufficient for getting the full experience of the talk, they may be useful after the talk, and they may help you decide whether or not you wish to attend the talk. In addition, the talk discusses a (probably) new proof of Viviani’s theorem, which is posted here. There is a also a brief reference to the use of a key example to understand the fundamental theorem of calculus, based on this paper. Finally, the talk references this video by 3 blue 1 brown that explains the circle division problem in about 9 minutes.

2. Former student Katy Smith (class of 2006) and I have a very nice result on vertex-magic total labelings of odd complete graphs. In fact we completely solved the spectrum problem for odd complete graphs, meaning that we described exactly the set of integers consisting of possible magic constants for vertex-magic total labelings of odd complete graphs. However, we also have a second much smaller paper with a similar sounding title, but on a different topic, with a much different result, on multiple complete graphs. Here is a preparing of this lesser known paper, Vertex magic total labelings of multiple complete graphs.

3. Another much older paper on vertex magic total labeling of cubic graphs, was a “major conceptual step forward,” according to the introduction of this paper. A preprint of the cubic graphs paper can be found here.

4. In April 2016, we had our baseball paper appear in Math Horizons. Here is an old version an arxiv of a preprint about the same topic, (but not done nearly as well as the Math Horizons version).

5. Our proof that every drawing of the complete graph in the plane must have at least 219 crossings is summarized on arxiv here. It is joint work with S. Pan and R. B. Richter. An improved version has since appeared and is available in JCT-B; the link to the improved version is here. In fact this new version was JCT-B’s hottest paper for July-September and October-December, 2015.

6. This preprint, Witt cancellation seen as a cancellation, is on the Witt Cancellation Theorem, with extra information about the Witt Ring. It is joint work with Sunil Chebolu and Ján Mináč. The illustrations are by Matthew Teigen. A different version of this paper has now been accepted for publication in Expositiones Mathematicae and it is available here.

7. Here are the slides for my talk, “Vertex-magic graphs,” from June 11, 2011, at the spring meeting of the Northeastern Section of the Mathematical Association of America.

 

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