相关论文: Combinatorial properties of Hechler forcing

Let G be a graph with a perfect matching. A complete forcing set of G is a subset of edges of G to which the restriction of every perfect matching is a forcing set of it. The complete forcing number of G is the minimum cardinality of…

Abstractly, the generic extensions after $\aleph_\omega$-many Cohen reals and $\aleph_{\omega+1}$-many Cohen reals must be different for reasons of uniform density the relevant Boolean algebras. Nevertheless this is not satisfying and it…

The celebrated Erd\H{o}s-Hajnal conjecture says that any graph without a fixed induced subgraph $H$ contains a very large homogeneous set. A direct analog of this conjecture is not true for hypergraphs. In this paper we present two natural…

The power-law behavior is ubiquitous in a majority of real-world networks, and it was shown to have a strong effect on various combinatorial, structural, and dynamical properties of graphs. For example, it has been shown that in real-life…

Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{CT}_{n}$ be the semigroup of full contractions on $[n]$. Denote $\mathcal{ORCT}_{n}$ and $\mathcal{OCT}_{n}$ to be the subsemigroup of order preserving or reversing and the…

In this paper we consider the Foreman's maximality principle, which says that any non-trivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We prove that it is…

It has been shown recently that the Eigenvector Method may lead to strong rank reversal in group decision making, that is, the alternative with the highest priority according to all individual vectors may lose its position when evaluations…

Let $G$ be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit $\check{\mathcal O}$ of $\check G$, the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic…

A theorem by Ding, Oporowski, Oxley, and Vertigan states that every sufficiently large bipartite graph without twins contains a matching, co-matching, or half-graph of any given size as an induced subgraph. We prove that this Ramsey…

Working in combinatorial model $\mathrm{W_{co}}(d)$, $d=1,2,\dots$, of P\'olya's random walker in $\mathbb{Z}^d$, we prove two theorems on recurrence to a vertex. We obtain an effective version of the first theorem if $d=2$. Using a…

We derive the joint asymptotic distribution of the outlier eigenvalues of an additively deformed Wigner matrix $H$. Our only assumptions on the deformation are that its rank be fixed and its norm bounded. Our results extend those of [The…

The Ramsey Choice principle for families of $n$-element sets, denoted $\mathrm{RC}_n$, states that every infinite set $X$ has an infinite subset $Y\subseteq X$ with a choice function on $[Y]^n := \{z\subseteq Y : |z| = n\}$. We investigate…

The paper is the second of our series of notes aimed to bring back in circulation some bright ideas of early modern set theory, mainly due to Harrington and Sami, which have never been adequately presented in set theoretic publications. We…

We prove that Real topological Hochschild homology can be characterized as the norm from the cyclic group of order $2$ to the orthogonal group $O(2)$. From this perspective, we then prove a multiplicative double coset formula for the…

This work studies the maximum possible sign rank of $N \times N$ sign matrices with a given VC dimension $d$. For $d=1$, this maximum is {three}. For $d=2$, this maximum is $\tilde{\Theta}(N^{1/2})$. For $d >2$, similar but slightly less…

For a field $\mathbb{F}$ and integers $d$ and $k$, a set ${\cal A} \subseteq \mathbb{F}^d$ is called $k$-nearly orthogonal if its members are non-self-orthogonal and every $k+1$ vectors of ${\cal A}$ include an orthogonal pair. We prove…

Stark-Heegner points are conjectural substitutes for Heegner points when the imaginary quadratic field of the theory of complex multiplication is replaced by a real quadratic field $K$. They are constructed analytically as local points on…

In this paper, we build some ergodic theorems involving function $\Omega$, where $\Omega(n)$ denotes the number of prime factors of a natural number $n$ counted with multiplicities. As a combinatorial application, it is shown that for any…

Occam's Razor tells us to pick the simplest model that fits our observations. In order to make sense of his process mathematically, we interpret it in the context of posets of functions. Our approach leads to some unusual new combinatorial…

Henselian elements are roots of polynomials which satisfy the conditions of Hensel's Lemma. In this paper we prove that for a finite field extension $(F|L,v)$, if $F$ is contained in the absolute inertia field of $L$, then the valuation…