Jay Cummings: Research Statement
نویسنده
چکیده
My research has touched many areas of combinatorics, including enumerative, algebraic, spectral, extremal and probabilistic. The projects below include finding the stationary distribution of a random coloring procedure, pursuing new directions in the math of juggling, working with undergraduates on Ramsey theory, and studying a pair of topics from spectral graph theory. I have mentored undergraduates on several research projects and throughout this statement I highlight many more problems suitable for undergraduates. I have submitted or published eight papers with at least three more in preparation. I very much enjoy collaboration and my Ph.D. advisor at UCSD is Ron Graham.
منابع مشابه
CALL FOR PAPERS Integrative and Translational Physiology: Integrative Aspects of Energy Homeostasis and Metabolic Diseases Ghrelin increases the motivation to eat, but does not alter food palatability
Joost Overduin, Dianne P. Figlewicz, Jennifer Bennett-Jay, Sepideh Kittleson, and David E. Cummings Veterans Administration Puget Sound Health Care System, Office of Research and Development Medical Research Service, Seattle, Washington; Division of Metabolism, Endocrinology and Nutrition, Department of Medicine, University of Washington School of Medicine, Seattle, Washington; Department of Ps...
متن کاملCospectral regular graphs with and without a perfect matching
For each b ≥ 5 we construct a pair of cospectral b-regular graphs, where one has a perfect matching and the other one not. This solves a research problem posed by the third author at the 22nd British Combinatorial Conference.
متن کاملACCF/ACR/AHA/ASE/ASNC/HRS/NASCI/RSNA/SAIP/SCAI/SCCT/SCMR 2008 Health Policy Statement on Structured Reporting in Cardiovascular Imaging. Endorsed by the Society of Nuclear Medicine [added].
2009;53;76-90; originally published online Dec 8, 2008; J. Am. Coll. Cardiol. Thomas, Peter L. Tilkemeier, and Wm. Guy Weigold Rosenthal, Harry Solomon, Arthur E. Stillman, Shawn D. Teague, James D. E. Kahn, Jr, Gerard R. Martin, Frederick A. Masoudi, Eric D. Peterson, Geoffrey L. McB. Hodgson, Udo Hoffmann, Robert J. Horn, III, W. Gregory Hundley, Charles Pamela S. Douglas, Robert C. Hendel, J...
متن کاملJuggling card sequences
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck paths, Narayana numbers, boson normal ordering, arc-labeled digraphs, and more. Some of these connections are investigated with a particular focus on enumerating...
متن کاملEdge flipping in the complete graph
We consider the following random process on the complete graph: repeatedly draw edges (with replacement) and with probability p assign the vertices of the edge blue and with probability 1 − p assign the vertices of the edge red. This is a random walk on a state space of red/blue colorings of the complete graph and so has a stationary distribution. We derive this stationary distribution as well ...
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