Related papers: Many partition relations below density

The dynamics of sedimenting particles under gravity are surprisingly complex due to the presence of effective long-ranged forces. When the particles are polar with a well-defined symmetry axis and non-uniform density, recent theoretical…

We establish the $\#P$-hardness of computing a broad class of immanants, even when restricted to specific categories of matrices. Concretely, we prove that computing $\lambda$-immanants of $0$-$1$ matrices is $\#P$-hard whenever the…

We investigate Tukey morphisms between binary relations, establishing several fundamental lemmas. We then specialize to finite binary relations, using computational methods to classify all binary relations with at most $6$ points in the…

Linearizing two partial orders to maximize the number of adjacencies and minimize the number of breakpoints is APX-hard. This holds even if one of the two partial orders is already a linear order and the other is an interval order, or if…

We examine the T-odd transverse lepton and $\Lambda$ polarizations in the baryonic decays of $\Lambda_b\to\Lambda l^+l^- (l=e ,\mu)$ to study the T violating effects. We show that the lepton polarizations are suppressed but the $\Lambda$…

The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical theorems. This idea leads to a new result generalizing…

We study surface plasmons localized on interfaces between topologically trivial and topologically non-trivial time reversal invariant materials in three dimensions. For the interface between a metal and a topological insulator the magnetic…

Cosmological perturbation equations derived from low-energy effective actions are shown to be invariant under a duality transformation reminiscent of electric-magnetic, strong-weak coupling, S-duality. A manifestly duality-invariant…

For an arbitrary finite dimensional algebra $\Lambda$, we prove that any wide subcategory of $\mathsf{mod} \Lambda$ satisfying a certain finiteness condition is $\theta$-semistable for some stability condition $\theta$. More generally, we…

We use $p$-rank bounds on partial ovoids and the classical bounds on Ramsey numbers to obtain upper bounds on the size of partial $m$-ovoids in finite classical polar spaces. These bounds imply non-existence of $m$-ovoids for new infinite…

Topological Ramsey spaces are spaces which support infinite dimensional Ramsey theory similarly to the Ellentuck space. Each topological Ramsey space is endowed with a partial ordering which can be modified to a $\sigma$-closed `almost…

We study dualities between classes of relational topological structures, given by Hom-functors. We show that there exists a 2-element structure with infinitely many relations, which reconstructs all other structures generated by a 2-element…

This essay builds on the idea of grouping the polar curves of 2-variable function germs into polar clusters. In the topological category, one obtains a bijective correspondence between certain partitions of the polar quotients of two…

We present a new model of sequential adsorption in which the adsorbing particles experience dipolar interactions. We show that in the presence of these long-range interactions, highly ordered structures in the adsorbed layer may be induced…

In two dimensional disordered lattices, presence of interaction makes particles less localized than the non-interacting ones within the range of disorder strength $W \le 4$ and interaction strength $V \le 4$. If the interaction strength is…

We consider the statistical mechanics of a system of topologically linked polymers, such as for instance a dense solution of polymer rings. If the possible topological states of the system are distinguished using the Gauss linking number as…

We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are in strong contact if a small enough object can pass from one of them to the other while remaining in their union. In the first half of the paper…

We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.

We study the doubly-polarized lepton pair forward-backward asymmetries in (Lambda_b -> Lambda l^+ l^-) decay using a general, model independent form of the effective Hamiltonian. We present the general expression for nine…

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the…