相关论文: Extreme lattices and vexillar designs

One of the important features of non-Hermitian Hamiltonians is the existence of a unique type of singularities, the so-called exceptional points (EPs). When the corresponding systems operate around such singularities, they exhibit…

We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…

In this article, we show that the minimal vectors of the extremal even unimodular lattices in $\mathbb{R}^{32}$ are $T$-avoiding universally optimal for suitable sets $T$. Moreover, they are minimal $T$-avoiding spherical designs and…

This paper surveys some recent results and progress on the extremal prob- lems in a given set consisting of all simple connected graphs with the same graphic degree sequence. In particular, we study and characterize the extremal graphs…

Let $M$ be an uniformizable Anderson $t$-motive of rank $r$, $L$ its lattice and $l_*:=\{l_1,\dots, l_r\}$ its basis. We define a map $\delta$ from the set of these bases to a flag variety (the present text gives the definition of $\delta$…

If K is an odd-dimensional flag closed manifold, flag generalized homology sphere or a more general flag weak pseudomanifold with sufficiently many vertices, then the maximal number of edges in K is achieved by the balanced join of cycles.…

For a $k$-uniform hypergraph $F$ let $\textrm{ex}(n,F)$ be the maximum number of edges of a $k$-uniform $n$-vertex hypergraph $H$ which contains no copy of $F$. Determining or estimating $\textrm{ex}(n,F)$ is a classical and central problem…

We consider the set of extremal points of the generalized unit ball induced by gradient total variation seminorms for vector-valued functions on bounded Euclidean domains. These are central to the understanding of sparse solutions and…

The application of flags to network coding has been introduced recently by Liebhold, Nebe, and Vazquez-Castro. It is a variant to random linear network coding and explicit routing solutions for given networks. Here we study lower and upper…

The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here…

Discrete subgroups of SL(2,R) are well understood, and classified by the geometry of the corresponding hyperbolic surfaces. Discrete subgroups of higher-rank semisimple Lie groups, such as SL(n,R) for n>2, remain more mysterious. While…

Experimental designs that spread out points apart from each other on projections are important for computer experiments when not necessarily all factors have substantial influence on the response. We provide a theoretical framework to…

Extreme economic outcomes are not shaped by tails alone. They are also shaped by unequal access to opportunities. This paper develops a theory of heterogeneous extremes by taking the distribution of opportunity access as the object of…

Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold developed an algorithm to enumerate, up to isomorphism, all finite lattices up to size 18.…

We study the rigidity in the sense of Zimmer for higher rank lattice actions on dendrites and show that: (1) if $\Gamma$ is a higher rank lattice and $X$ is a nondegenerate dendrite with no infinite order points, then any action of $\Gamma$…

For L a finite lattice, let C(L) denote the set of pairs g = (g_0,g_1) such that g_0 is a lower cover of g_1 and order it as follows: g <= d iff g_0 <= d_0, g_1 <= d_1, but not g_1 <= d_0. Let C(L,g) denote the connected component of g in…

In the paper we generalize the notion of problem (P) introduced by Poletsky. We introduce the notion of (P_m) extremals. For example, geodesics are (P_1) extremals. Using obtained results we present a description of (P_m) extremals in…

The hyperoctahedral group $H$ in $n$ dimensions (the Weyl group of Lie type $B_n$) is the subgroup of the orthogonal group generated by all transpositions of coordinates and reflections with respect to coordinate hyperplanes. A finite set…

Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast,…

The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…