Related papers: Stanley's Major Contributions to Ehrhart Theory

This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.

In these notes I will review the results that have been obtained in these last years on the computation of the number of metastable states in infinite-range models of disordered systems. This is a particular case of the problem of computing…

We establish strict growth for the rank function of an r-differential poset. We do so by exploiting the representation theoretic techniques developed by Reiner and the author for studying related Smith forms.

In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…

We give a short appreciation of Robin Milner's seminal contributions to the theory of concurrency.

Regarding Euler's odd-strict theorem, which is the most basic partition identity, A refinement was done by Sylvester, and it was generalized by Bessenrodt to the r-regular and r-class regular cases. In this paper, we focus on the…

BRST-methods provide elegant and powerful tools for the construction and analysis of constrained systems, including models of particles, strings and fields. These lectures provide an elementary introduction to the ideas, illustrated with…

Let $I\supsetneq J$ be two monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . We study when the Stanley Conjecture holds for $I/J$ using the recent result of \cite{IKM} concerning the…

We establish a variety of extensions to the Erdos-Rado Theorem, particularly involving ordinal numbers, and always involving ordinary partition relations. Most of the results can be regarded as consequences of the Ramification Principle,…

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…

We give a geometric interpretation of the Stanley--Reisner correspondence, extend it to schemes, and interpret it in terms of the field of one element.

This is primarily an exposition of our work on Hardy algebras associated with $W^*$-correspondences with an emphasis on interpolation results (a generalized Nevanlinna-Pick theorem) and the concepts of Schur class operator functions (and…

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.

We study spherical tetrahedra with rational dihedral angles and rational volumes. Such tetrahedra occur in the Rational Simplex Conjecture by Cheeger and Simons, and we supply vast families, discovered by computational efforts, of positive…

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika…

We establish a formalism for working with incidence algebras of posets with symmetries, and we develop equivariant Kazhdan-Lusztig-Stanley theory within this formalism. This gives a new way of thinking about the equivariant Kazhdan-Lusztig…

Linear combinations of exponentials $e^{i\lambda_kt}$ in the case where the distance between some points $\lambda_k$ tends to zero are studied. D. Ullrich has proved the basis property of the divided differences of exponentials in the case…

We prove an estimate on the number of rational points on the Grassmannian variety of bounded twisted height, refining the classical results of Schmidt ([12]) and Thunder ([20]) over the rational field: most importantly, our formula counts…