He began pulling in different areas of math outside of combinatorics, including finite geometry, algebra and probability. From Science Daily They enlisted software developer Joseph Samuel Myers and University of Arkansas mathematician Chaim Goodman-Strauss, who had both worked with tiling and combinatoric...
-dense in the uniform distribution, meaning that every point has probability at most . Observe also that we have for every , because and have the same sign and , so we have and sois a hardcore distribution, because the above expression is equivalent to ...
U. Pierce, Combinatorics of dispersionless integrable systems and universality in random matrix theory, Commun. Math. Phys. 292 (2009) 529.Y.Kodama, V.Pierce, Combinatorics of dispersionless integrable systems and universality in random matrix theory, IMRN 2007, no. 23, Art. ID rnm120, 55 pp...
We show that they can be calculated using an explicit formula that includes the sum of the binomial coefficients and has a clear geometric meaning. In addition, we consider two different generating function for the universal coefficients. One of them, up to normalization, has the simple form of...
•page45,line1.Change w to T(w).•page47,line11.Change n≥2to n≥1.•page49,lines20–22.The two sentence beginning“Figure1.10...”and“Let f(n)denote...”should be interchanged,since f(n)is used in thefirst of these sentences but defined in the second.•page50,...
As we will see, it has deeper geometric and topological meaning as well: (1) It tells us about the tangent spaces at each permutation flag in each Schubert variety. (2) It tells us about singular points in Schubert varieties. (3) It tells us about the values of Kostant polynomials. ...
One can derive from the matchings model an enumerative meaning for the Markoff numbers, and prove that the associated Laurent polynomials have positive coefficients as was conjectured (much more generally) by Fomin and Zelevinsky. Most of this research was conducted under the auspices of REACH (...
Studies in Applied MathematicsLabelle, J., Yeh, Y.N.: The combinatorics of Laguerre, Charlier, and Hermite polynomials. Stud. Appl. Math. 80 , 25–36 (1989)J. Labelle and Y. N. Yeh., The combinatorics of Laguerre, Charlier and Hermite polynomials, Studies in Applied Math. 80 (1989),...
,jkA)∈A′, meaning that G⋏rkA is not (kA,rkB)-colorable. ◻ 3.2 Asymptotic Existence for Complete Bipartite Graphs For this subsection, we return to the case when G=KΔB,ΔA is complete bipartite. In this case, Lemma 3.5 rewrites as follows: Corollary 3.6 If G=KΔB,ΔA is ...
Combinatorial identities usually have more than one possible proof. Some of them are analytic, some algebraic in nature, but the most beautiful ones are combinatorial, meaning that both sides of the identity count the same set of elements in different ways. ...