相关论文: The Topological Tverberg Problem and winding numbe…

As we known, the {\it Seifert-Van Kampen theorem} handles fundamental groups of those topological spaces $X=U\cup V$ for open subsets $U, V\subset X$ such that $U\cap V$ is arcwise connected. In this paper, this theorem is generalized to…

We introduce a homological approach to exhibiting instances of Stembridge's q=-1 phenomenon. This approach is shown to explain two important instances of the phenomenon, namely that of partitions whose Ferrers diagrams fit in a rectangle of…

A conjecture of Coleman implies that only finitely many quaternion algebras over the rational numbers can be the endomorphism $\mathbf{Q}$-algebras of abelian surfaces over the complex numbers which can be defined over $\mathbf{Q}$. One may…

The $3x+1$ Conjecture asserts that the $T$-orbit of every positive integer $x$ contains $1$, where $T$ maps $x$ to $x/2$ for $x$ even and to $(3x+1)/2$ for $x$ odd. Several authors have studied the analogous map, $T_q$, which maps $x\in…

The Terwilliger algebra $T(x)$ of a finite connected simple graph $\Gamma$ with respect to a vertex $x$ is the complex semisimple matrix algebra generated by the adjacency matrix $A$ of $\Gamma$ and the diagonal matrices…

For a finite set $S$ of points in the plane and a graph with vertices on $S$ consider the disks with diameters induced by the edges. We show that for any odd set $S$ there exists a Hamiltonian cycle for which these disks share a point, and…

The purpose of this article is to show uniqueness theorems for meromorphic mappings of C^m to CP^n with few hyperplanes H_j, j=1,...,q. It is well known that uniqueness theorems hold for q \geq 3n+2. In this paper we show that for every…

The well-known Reifenberg theorem states that if a subset of $\mathbb{R}^n$ can be well approximated by $k$-planes at every point and every scale, then it is biH\"older homeomorphic to a $k$-disk. This article concerns a subset $S$ of…

Let $T$ be a tree with $t$ edges. We show that the number of isomorphic (labeled) copies of $T$ in a graph $G = (V,E)$ of minimum degree at least $t$ is at least \[2|E| \prod_{v \in V} (d(v) - t + 1)^{\frac{(t-1)d(v)}{2|E|}}.\]…

Tait's flyping conjecture, stating that two reduced, alternating, prime link diagrams can be connected by a finite sequence of flypes, is extended to reduced, alternating, prime diagrams of 4-regular graphs in S^3. The proof of this version…

Ehrenborg noted that all tilings of a bipartite planar graph are encoded by its cubical matching complex and claimed that this complex is collapsible. We point out to an oversight in his proof and explain why these complexes can be the…

We adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the…

The program of understanding Shape Theory layer by layer topologically and geometrically -- proposed in Part I -- is now addressed for 4 points in 1-$d$. Topological shape space graphs are far more complex here, whereas metric shape spaces…

Let $q=p^e$, where $p$ is a prime and $e\geq 1$ is an integer. For $m\geq 1$, let $P$ and $L$ be two copies of the $(m+1)$-dimensional vector spaces over the finite field $\mathbb{F}_q$. Consider the bipartite graph $W_m(q)$ with partite…

Jacobian conjectures (that nonsingular implies invertible) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The associated…

In this paper we give an asymptotically tight bound for the tolerated Tverberg Theorem when the dimension and the size of the partition are fixed. To achieve this we study certain partitions of order-type homogeneous sets and use a…

A famous conjecture of Ryser is that in an $r$-partite hypergraph the covering number is at most $r-1$ times the matching number. If true, this is known to be sharp for $r$ for which there exists a projective plane of order $r-1$. We show…

In this paper, we prove a version of the Colored Tverberg Theorem with new constraints on the faces, in which we limit the number of faces with each one of the colors.

We show that any point in the convex hull of each of (d+1) sets of (d+1) points in general position in \R^d is contained in at least (d+1)^2/2 simplices with one vertex from each set. This improves the known lower bounds for all d >= 4.

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…