Related papers: Infinite Partitions and Rokhlin Towers

Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to…

Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…

It is consistent that there is a partial order (P,<) of size aleph_1 such that every monotone (unary) function from P to P is first order definable in (P,<). The partial order is constructed in an extension obtained by finite support…

We obtain partition regularity results for homogeneous quadratic equations whose parametrized solutions admit nice factorizations into linear forms over rings of integers of imaginary quadratic fields. To do so, we develop number-theoretic…

Finding classical canonical observables consists of taking a function space over phase space. For constrained theories, these functions must form zero brackets with a closed algebraic structure of first-class constraints. This brackets…

We prove a weak-type (1,1) inequality for square functions of non-commutative martingales that are simultaneously bounded in $L^2$ and $L^1$. More precisely, the following non-commutative analogue of a classical result of Burkholder holds:…

We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral…

In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about…

We construct new examples of inclusions of unital $C\sp*$-algebras of index-finite type with the Rokhlin property motivated by a broader attempt to understand the range of such inclusions beyond known models. In the course of this…

Stanley defined a partition function t(n) as the number of partitions $\lambda$ of n such that the number of odd parts of $\lambda$ is congruent to the number of odd parts of the conjugate partition $\lambda'$ modulo 4. We show that t(n)…

This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…

The distinguishing number of a structure is the smallest size of a partition of its elements so that only the trivial automorphism of the structure preserves each cell of the partition. We show that for any countable subset of the positive…

We prove the existence of harmonic functions $f$ on trees, with respect to suitable transient transition operators $P$, that satisfy an analogue of Menshov universal property in the following sense: $f$ is the Poisson transform of a…

Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colourings or the number of independent sets of a graph and also the partition…

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length $\omega$ to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite…

In this article, we introduce the notion of almost consecutive partitions. A partition is almost consecutive if every term is consecutive, with the possible exception of the smallest one. We find formulas relating to the smallest parts of…

We study the rich behavior of ergodicity and conservativity of Cartesian products of infinite measure preserving transformations. A class of transformations is constructed such that for any subset $R\subset \mathbb Q\cap (0,1)$ there exists…

We continue the investigation of analytic spaces from the perspective of computable structure theory. We show that if $p \geq 1$ is a computable real, and if $\Omega$ is a nonzero, non-atomic, and separable measure space, then every…