Related papers: Hypergraphs and proper forcing

The pantograph differential equation and its solution, the deformed exponential function, are remarkable objects that appear in areas as diverse as combinatorics, number theory, statistical mechanics, and electrical engineering. In this…

We study forcing pairs for quasirandom graphs. Chung, Graham, and Wilson initiated the study of families $\\mathcal F$ of graphs with the property that if a large graph $G$ has approximately homomorphism density $p^{e(F)}$ for some fixed…

We prove the existence of a sequence of commutative diagrams generalizing existing results on the cohomology of the Borel-Serre boundary and well-rounded retract to the context of the well-tempered complex. Our main theorem provides a…

The aim of this short note is to communicate a simple solution to the problem posed in [1] as Question 7.2.7: is it true that for every ccc $\sigma$-ideal I any I-positive Borel set contains modulo I an I-positive closed set?

A forcing set for a perfect matching of a graph is defined as a subset of the edges of that perfect matching such that there exists a unique perfect matching containing it. A complete forcing set for a graph is a subset of its edges, such…

We consider ``meager analogues'' of classical covering properties of Menger, Hurewicz and Rothberger. We show that Borel images of sets having ``our'' covering properties have these classical covering properties.

Let $\mathrm{G}$ be a subgroup of the symmetric group $\mathfrak S(U)$ of all permutations of a countable set $U$. Let $\overline{\mathrm{G}}$ be the topological closure of $\mathrm{G}$ in the function topology on $U^U$. We initiate the…

For a hypergraph $\mathbb{H}$ on $[n]$, the hypergraphic poset $P_\mathbb{H}$ is the transitive closure of the oriented $1$-skeleton of the hypergraphic polytope $\Delta_\mathbb{H}$. In a recent paper, N. Bergeron and V. Pilaud provided a…

Specht polynomials classically realize the irreducible representations of the symmetric group. The ideals defined by these polynomials provide a strong connection with the combinatorics of Young tableaux and have been intensively studied by…

The `Weyl symmetric functions' studied here naturally generalize classical symmetric (polynomial) functions, and `Weyl bialternants,' sometimes also called Weyl characters, analogize the Schur functions. For this generalization, the…

Let $X$ be an uncountable Polish space and let $\mathcal{I}$ be an ideal on $\omega$. A point $\eta \in X$ is an $\mathcal{I}$-limit point of a sequence $(x_n)$ taking values in $X$ if there exists a subsequence $(x_{k_n})$ convergent to…

Let $G$ be a relatively hyperbolic group that admits a decomposition into a finite graph of relatively hyperbolic groups structure with quasi-isometrically (qi) embedded condition. We prove that the set of conjugates of all the vertex and…

Etzion et al. introduced metrics on $\mathbb{F}_2^n$ based on directed graphs on $n$ vertices and developed some basic coding theory on directed graph metric spaces. In this paper, we consider the problem of classifying directed graphs…

We study dismantlability in graphs. In order to compare this notion to similar operations in posets (partially ordered sets) or in simplicial complexes, we prove that a graph G dismants on a subgraph H if and only if H is a strong…

The $(P, \omega)$-partition generating function of a labeled poset $(P, \omega)$ is a quasisymmetric function enumerating certain order-preserving maps from $P$ to $\mathbb{Z}^+$. We study the expansion of this generating function in the…

For any contractive iterated function system (IFS, including the Moran systems), we show that there is a natural hyperbolic graph on the symbolic space, which yields the H\"{o}lder equivalence of the hyperbolic boundary and the invariant…

We expand the results of Roslanowski and Shelah arXive:1806.06283 , arXive:1909.00937 to all perfect Abelian Polish groups $(H,+)$. In particular, we show that if $\alpha<\omega_1$ and $4\leq k<\omega$, then there is a ccc forcing notion…

Given a directed graph, an equivalence relation on the graph vertex set is said to be balanced if, for every two vertices in the same equivalence class, the number of directed edges from vertices of each equivalence class directed to each…

For a given partially ordered set (poset) and a given family of mappings of the poset into itself, we study the problem of the description of joint fixed points of this family. Well-known Tarski's theorem gives the structure of the set of…

Let $\pi:{\mathbb R}^n \to {\mathbb R}^d$ be any linear projection, let $A$ be the image of the standard basis. Motivated by Postnikov's study of postitive Grassmannians via plabic graphs and Galashin's connection of plabic graphs to slices…