Related papers: Packing A-Paths of Length Zero Modulo Four

We show that in each dimension $4n+3$, $n\ge 1$, there exist infinite sequences of closed smooth simply connected manifolds $M$ of pairwise distinct homotopy type for which the moduli space of Riemannian metrics with nonnegative sectional…

Duke and the second author defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half integral weight and level 4 and…

We show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities), i.e. monopoles on $\mathbb{R}^{2} \times \mathbb{S}^{1}$ possibly singular at a finite collection of points, are either empty or…

Given a graph $G$ and $\mathcal{A}\subseteq V(G)$, a classical theorem of Gallai (1964) states that for every positive integer $k$, the graph $G$ contains $k$ pairwise vertex-disjoint $\mathcal{A}$-paths, or a set $Z\subseteq V(G)$ of size…

It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SL_q(2)) is a free module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided.

We prove that a closed 4-manifold has shadow-complexity zero if and only if it is a kind of 4-dimensional graph manifold, which decomposes into some particular blocks along embedded copies of S^2 x S^1, plus some complex projective spaces.…

For a graph $H$, we say that $H$ has the Erd\H{o}s-P\'osa property for subdivisions with function $f$, if for every graph $G$, either $G$ contains (as a subgraph) $k+1$ pairwise disjoint subdivisions of $H$ or there exists a set $X\subseteq…

We examine the following fourth order H\'enon equation \label{pipe} \Delta^2 u = |x|^\alpha u^p \qquad \text{in}\ \IR^N, where $ 0 < \alpha$. Define the Hardy-Sobolev exponent $ p_4(\alpha):= \frac{N+4 + 2 \alpha}{N-4}$. We show that in…

Quantum corrections can severely modify or even remove classical infinite distance limits in four-dimensional gravity theories with minimal N=1 supersymmetry. In this note we study this effect for infinite distance directions in the…

Let $\Omega$ be a connected open set in the plane and $\gamma: [0,1] \to \overline{\Omega}$ a path such that $\gamma((0,1)) \subset \Omega$. We show that the path $\gamma$ can be ``pulled tight'' to a unique shortest path which is homotopic…

Answering a question of P. Erdos from 1965, we show that for every eps>0 there is a set A of n integers with the following property: every subset A' of A with at least (1/3 + eps)n elements contains three distinct elements x,y,z with x + y…

Let $p$ be any odd prime number. Let $k$ be any positive integer such that $2\leq k\leq [\frac{p+1}3]+1$. Let $S = (a_1,a_2,...,a_{2p-k})$ be any sequence in ${\Bbb Z}_p$ such that there is no subsequence of length $p$ of $S$ whose sum is…

A sequence in the additive group ${\mathbb Z}_n$ of integers modulo $n$ is called $n$-zero-free if it does not contain subsequences with length $n$ and sum zero. The article characterizes the $n$-zero-free sequences in ${\mathbb Z}_n$ of…

We find the shape of the Donaldson invariants of a 4-manifold with b_1=0 and b^+>1, which may be not of simple type. The invariants appear as the q^0 coefficient of a expression given in terms of modular forms (as was predicted by Moore and…

Popa and Schnell show that any holomorphic 1-form on a smooth projective variety of general type has zeros. In this article, we show that a smooth good minimal model has a holomorphic 1-form without zero if and only if it admits an analytic…

In 1959, Marcus and Ree proved that any bistochastic matrix $A$ satisfies $\Delta_n(A):= \max_{\sigma\in S_n}\sum_{i=1}^{n}A(i, \sigma(i))-\sum_{i, j=1}^n A(i, j)^2 \geq 0$. Erd\H{o}s asked to characterize the bistochastic matrices…

Grids with blocked and unblocked cells are often used to represent terrain in robotics and video games. However, paths formed by grid edges can be longer than true shortest paths in the terrain since their headings are artificially…

We consider the length $L(n)$ of the longest path in a randomly generated Apollonian Network (ApN) ${\cal A}_n$. We show that w.h.p. $L(n)\leq ne^{-\log^cn}$ for any constant $c<2/3$.

This is the addendum to the paper "On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra" Communications in Algebra, 40:6 (2012), 2005-2036 (DOI: 10.1080/00927872.2011.570830). We give here the full proof of…

We show that the plane Cremona group over a field of characteristic p > 0 does not contain elements of order of power of p larger than 2 and it does not contain elements of order p^2 unless p =2. Also we describe conjugacy classes of…