Related papers: Additive Entropies of Partitions
The elementary symmetric partition function is a map on the set of partitions. It sends a partition lambda to the partition whose parts are the summands in the evaluation of the elementary symmetric function on the parts of lambda. These…
We consider the computational aspects of lossy data compression problem, where the compression error is determined by a cover of the data space. We propose an algorithm which reduces the number of partitions needed to find the entropy with…
The investigation of partitions of integers plays an important role in combinatorics and number theory. Among the many variations, partitions into powers $0<\alpha<1$ were of recent interest. In the present paper we want to extend our…
This work examines some aspects related to the existence of negative mass. The requirement for the partition function to converge leads to two distinct approaches. Initially, convergence is achieved by assuming a negative absolute…
The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…
In this expository paper we summarize the connection between random partitions and 4-dimensional supersymmetric gauge theories discovered in hep-th/0306238. There is also a brief section about how this extends to 3-dimensional partitions…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
The article is devoted to stochastic processes with values in finite-dimensional vector spaces over infinite locally compact fields with non-trivial non-archimedean valuations. Infinitely divisible distributions are investigated. Theorems…
Let $\cal{N}=\{1,\cdots,n\}$. The entropy function $\bf h$ of a set of $n$ discrete random variables $\{X_i:i\in\cal N\}$ is a $2^n$-dimensional vector whose entries are ${\bf{h}}({\cal{A}})\triangleq H(X_{\cal{A}}),\cal{A}\subset{\cal N}…
Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective…
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…
Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail…
For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.
The minimum entropy output is computed for rotationally invariant quantum channels acting on spin-1/2 and spin-1 systems. For the case of two parallel such channels and initial entangled (singlet) state the entropy of the output is higher…
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
We extend the theory of infinite-exponent partition relations to arbitrary linear order types, with a particular focus on the real number line. We give a complete classification of all consistent partition relations on the real line with…
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…
An inequality for the variance of an additive function defined on random decomposable structures, called assemblies, is established. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set…