17 citations · 51 across the 22 of their papers we have counts for
26 papers
Inverse Participation Ratios in the XX spin chain
Emmanuel Tsukerman
We continue the study of the Inverse Participation Ratios (IPRs) of the XXZ Heisenberg spin chain initiated by Misguich, Pasquier and Luck (2016) by focusing on the case of the XX…
A General Method to Determine Limiting Optimal Shapes for Edge-Isoperimetric Inequalities
Emmanuel Tsukerman, Ellen Veomett
For a general family of graphs on , we translate the edge-isoperimetric problem into a continuous isoperimetric problem in . We then solve the continuou…
Extension of the first mixed volume to nonconvex sets
Emmanuel Tsukerman
We study the first mixed volume for nonconvex sets and apply the results to limits of discrete isoperimetric problems. Let . Define $D_N (M)=\lim_{ε\down…
A Simple Proof of Cauchy's Surface Area Formula
Emmanuel Tsukerman, Ellen Veomett
We give a short and simple proof of Cauchy's surface area formula, which states that the average area of a projection of a convex body is equal to its surface area up to a multipli…
Symmetric matrices, Catalan paths, and correlations
Bernd Sturmfels, Emmanuel Tsukerman, Lauren Williams
Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almost-principal minors. Each entry is an explicit Laurent polynomi…
Iterating evolutes and involutes
M. Arnold, D. Fuchs, I. Izmestiev +2
We study iterations of two classical constructions, the evolutes and involutes of plane curves, and we describe the limiting behavior of both constructions on a class of smooth cur…
Dimension of gram spectrahedra of univariate polynomials
Emmanuel Tsukerman
The Gram Spectrahedron of a polynomial parametrizes its sums-of-squares representations. In this note, we determine the dimension of Gram Spectrahedra of univariate polynomials.
Equality of Dedekind sums mod
Emmanuel Tsukerman
Using a generalization due to Lerch [M. Lerch, Sur un théorème de Zolotarev. Bull. Intern. de l'Acad. François Joseph 3 (1896), 34-37] of a classical lemma of Zolotarev, employed i…
Tropical Spectral Theory of Tensors
Emmanuel Tsukerman
We introduce and study tropical eigenpairs of tensors, a generalization of the tropical spectral theory of matrices. We show the existence and uniqueness of an eigenvalue. We assoc…
Remarks on the the circumcenter of mass
S. Tabachnikov, E. Tsukerman
Suppose that to every non-degenerate simplex Delta in n-dimensional Euclidean space a `center' C(Delta) is assigned so that the following assumptions hold: (i) The map that assigns…
Equality of Dedekind sums mod and
Emmanuel Tsukerman
In [Girstmair, A criterion for the equality of Dedekind sums mod , Internat. J. Number Theory 10: (2014) 565--568], it was shown that the necessary condition $b \mid (a…
Determining the maximum difference between the number of atoms and number of coatoms of a Bruhat interval of the symmetric group
Emmanuel Tsukerman
We determine the largest difference between the number of atoms and number of coatoms of a Bruhat interval of .
Bruhat Interval Polytopes
Emmanuel Tsukerman, Lauren Williams
Let u and v be permutations on n letters, with u <= v in Bruhat order. A Bruhat interval polytope Q_{u,v} is the convex hull of all permutation vectors z = (z(1), z(2),...,z(n)) wi…
The -adic Order of Power Sums, the Erdös-Moser Equation, and Bernoulli Numbers
Jonathan Sondow, Emmanuel Tsukerman
The Erdös-Moser equation is a Diophantine equation proposed more than 60 years ago which remains unresolved to this day. In this paper, we consider the problem in terms of divisibi…
On symplectic capacities of toric domains
Michael Landry, Matthew McMillan, Emmanuel Tsukerman
A toric domain is a subset of which is invariant under the standard rotation action of on . For a toric domain from…
Polygonal Bicycle Paths and the Darboux Transformation
I. Alevy, E. Tsukerman
A Bicycle -gon is an equilateral -gon whose diagonals are of equal length. In this paper we consider periodic bicycle -paths, which are a natural variation in…
Fourier-Dedekind Sums and an Extension of Rademacher Reciprocity
Emmanuel Tsukerman
Fourier-Dedekind sums are a generalization of Dedekind sums - important number-theoretical objects that arise in many areas of mathematics, including lattice point enumeration, sig…
Monotonicity of the optimal perimeter in isoperimetric problems on
Emmanuel Tsukerman
We prove general theorems for isoperimetric problems on lattices of the form which state that the perimeter of the optimal set is a monot…
Circumcenter of Mass and generalized Euler line
Serge Tabachnikov, Emmanuel Tsukerman
We define and study a variant of the center of mass of a polygon and, more generally, of a simplicial polytope which we call the Circumcenter of Mass (CCM). The Circumcenter of Mas…
Discrete Conics
Emmanuel Tsukerman
In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise…
On the discrete bicycle transformation
Serge Tabachnikov, Emmanuel Tsukerman
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the contin…
Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos
Emmanuel Tsukerman
In a recent paper titled "The parbelos, a parabolic analog of the arbelos", Sondow asks for a synthetic proof to the tangency property of the parbelos. In this paper, we resolve th…
The Edge-Isoperimetric Problem in
Emmanuel Tsukerman
We consider the edge-isoperimetric problem on the graph of the infinite grid in the metric. We first show that the solutions are not nested, so tha…
The Perpendicular Bisector Construction in -dimensional Euclidean and Non-euclidean Geometries
Emmanuel Tsukerman
The "Perpendicular Bisectors Construction" is a natural way to seek a replacement for the circumcenter of a noncyclic quadrilateral in the plane. In this paper, we generalize this…