相关论文: Mallows Permutations and Finite Dependence
We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…
We show the existence of several infinite monochromatic patterns in the integers obtained as values of suitable symmetric polynomials. The simplest example is the following. For every finite coloring of the natural numbers…
This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be…
We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with colored vertices, in which we fix the degree sequence and…
We study the infinite graph of $n$-dimensional rectangular grid that doesn't appear distance regular and the distance regular colorings of this graph, which are defined as the distance colorings with respect to completely regular codes. It…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
In this short article, we study factor colorings of aperiodic linearly recurrent infinite words. We show that there always exists a coloring which does not admit a monochromatic factorization of the word into factors of increasing lengths.
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring…
We present an explicit family of hypergraphs with arbitrarily large uniformity and chromatic number that admit realizations in both geometric and number-theoretic settings. As an application, we give a new proof of a theorem of Chen, Pach,…
We conduct a computability-theoretic study of Ramsey-like theorems of the form "Every coloring of the edges of an infinite clique admits an infinite sub-clique avoiding some pattern", with a particular focus on transitive patterns. As it…
We prove that a wide range of coloring problems in graphs on surfaces can be resolved by inspecting a finite number of configurations.
We show that an effective version of Siegel's Theorem on finiteness of integer solutions and an application of elementary Galois theory are key ingredients in a complexity classification of some Holant problems. These Holant problems,…
The paper is devoted to the study of mappings with finite distortion, actively studied recently. For mappings whose inverse satisfy the Poletsky inequality, the results on boundary behavior in terms of prime ends are obtained. In…
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…
We consider a particle system on $Z^d$ with finite state space and interactions of infinite range. Assuming that the rate of change is continuous and decays sufficiently fast, we introduce a perfect simulation algorithm for the stationary…
Marked mesh patterns are a very general type of permutation pattern. We examine a particular marked mesh pattern originally defined by Kitaev and Remmel, and show that its generating function is described by the $r$-Stirling numbers. We…
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
Raimi's theorem guarantees the existence of a partition of $\mathbb{N}$ into two parts with an unavoidable intersection property: for any finite coloring of $\mathbb{N}$, some color class intersects both parts infinitely many times, after…
In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.
We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical…