相关论文: Polygon dissections and some generalizations of cl…

We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…

In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators $L=p^n+\sum_{j=-\infty}^{n-1}u_j p^j$. The reduction of the Poisson…

We first construct the total simplicial complex (TSC) of a finite simple graph $G$ in order to generalize the total graph $T(G)$. We show that $\Delta_T(G)$ is not Cohen-Macaulay (CM) in general. For a connected graph $G$, we prove that the…

The $m$-neighbor complex of a graph is the simplicial complex in which faces are sets of vertices with at least $m$ common neighbors. We consider these complexes for Erdos-Renyi random graphs and find that for certain explicit families of…

We derive sufficient conditions under which the ``second'' Hamiltonian structure of a class of generalized KdV-hierarchies defines one of the classical $\cal W$-algebras obtained through Drinfel'd-Sokolov Hamiltonian reduction. These…

We define and study a simplicial complex which is a homogeneous space for the group $PGL(2, K)$ over a two-dimensional local field $K$. The complex is a generalization of the tree studied by F. Bruhat, J. Tits, J.-P. Serre and P. Cartier in…

Combining Elliott, Gong, Lin and Niu's result and Castillejos and Evington's result, we see that if $A$ is a simple separable nuclear monotracial C$^*$-algebra, then $A\otimes\mathcal{W}$ is isomorphic to $\mathcal{W}$ where $\mathcal{W}$…

Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into…

The cosimplicial scheme $$Delta^bullet = \Delta^0 smallmatrix \to smallmatrix \Delta^1 smallmatrix to smallmatrix ...;\quad \Delta^n :=\Spec\Big(k[t_0,...c,t_n]/(\sum t_i -t)\Big)$$ was used in B to define higher Chow groups. In this note,…

Let $W$ be a domain in a connected complex manifold $M$ and $w_0\in W$. Let ${\mathcal A}_{w_0}(W,M)$ be the space of all continuous mappings of a closed unit disk $\overline D$ into $M$ that are holomorphic on the interior of $\overline…

Forman introduced discrete Morse theory as a tool for studying CW complexes by essentially collapsing them onto smaller, simpler-to-understand complexes of critical cells in [Fo]. Chari reformulated discrete Morse theory for regular cell…

H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials (H. Widom. J. Stat. Phys. 94, (1999) 347-363). We obtain similar results for discrete…

We classify all groups G and all pairs (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the support of the direct sum of V and W generates G, the square of the braiding between V and W is not the identity, and the Nichols…

The family of Buchsbaum simplicial posets generalizes the family of simplicial cell manifolds. The $h'$-vector of a simplicial complex or simplicial poset encodes the combinatorial and topological data of its face numbers and the reduced…

Consider an absolutely simple abelian variety A defined over a number field K. For most places v of K, we study how the reduction A_v of A modulo v splits up to isogeny. Assuming the Mumford-Tate conjecture for A and possibly increasing K,…

Let Delta_{n-1} denote the (n-1)-dimensional simplex. Let Y be a random k-dimensional subcomplex of Delta_{n-1} obtained by starting with the full (k-1)-dimensional skeleton of Delta_{n-1} and then adding each k-simplex independently with…

In attempting to understand how combinatorial modifications alter algebraic properties of monomial ideals, several authors have investigated the process of adding "whiskers" to graphs. In this paper, we study a similar construction to build…

We translate the operations of polarization and depolarization from monomial ideals in a polynomial ring to abstract simplicial complexes. As a result, we explicitly describe the relation between the Koszul simplicial complex of a monomial…

Given a finite set of points in $\mathbb R^n$ and a radius parameter, we study the \v{C}ech, Delaunay-\v{C}ech, Delaunay (or Alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the \v{C}ech and…

The prime spectra of two families of algebras, $S^w$ and $\check{S}^w$, $w\in W,$ indexed by the Weyl group $W$ of a semisimple finitely dimensional are studied. The algebras $S^w$ have been introduced by A.~Joseph; they are $q$-analogues…