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- Matthias Beck, Pallavi Jayawant, Tyrrell B. McAllister
- J. Comb. Theory, Ser. A
- 2012

Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give formulas for the generating… (More)

We provide a combinatorial proof of the trigonometric identity cosðny Þ¼ TnðcosyÞ, where Tn is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric… (More)

Combinatorial and Umbral Methods for Orthogonal Polynomials A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University, Waltham, Massachusetts

The minimum spanning tree problem originated in the 1920s when O. Borůvka identified and solved the problem during the electrification of Moravia. This graph theory problem and its numerous… (More)

Tucker's Lemma is a combinatorial analog of the Borsuk-Ulam theorem and the case n=2 was proposed by Tucker in 1945. Numerous generalizations and applications of the Lemma have appeared since then.… (More)

- Ira M. Gessel, Pallavi Jayawant
- Electr. J. Comb.
- 2004

Some of the classical orthogonal polynomials such as Hermite, Laguerre, Charlier, etc. have been shown to be the generating polynomials for certain combinatorial objects. These combinatorial… (More)

In this note, we give an elementary and combinatorial analog of a result of Freeman J. Dyson. We also show that our result is equivalent to Dyson’s theorem.

Charlier configurations provide a combinatorial model for Charlier polynomials. We use this model to give a combinatorial proof of a multilinear generating function for Charlier polynomials. As… (More)

- Matt Côté co-chair, Pallavi Jayawant, Hong Lin co-chair, R J Sommer
- 2009

The team tasked in October 2009 with heading the President's initiative entitled "the Natural Sciences and Mathematics in the Liberal Arts" began by asking itself what the phrase “science and… (More)