Related papers: Additive Entropies of Partitions
An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…
In this paper, we obtain upper and lower bounds for the partition function $p(n)$ by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.
Let $\mathcal{R}$ be a commutative ring with unity, and let $P$ be a locally finite poset. The aim of the paper is to provide an explicit description of the additive biderivations of the incidence algebra $I(P, \mathcal{R})$. We demonstrate…
In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…
We show that counting different configurations that give rise to black hole entropy in loop quantum gravity is related to partitions in number theory.
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction…
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…
Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further. We calculate the probability for an arbitrary path followed by a system…
This paper studies properties of entropy functions that are induced by groups and subgroups. We showed that many information theoretic properties of those group induced entropy functions also have corresponding group theoretic…
In this note we present that the patch counting entropy can be obtained as a limit and investigate which sequences of compact sets are suitable to define this quantity. We furthermore present a geometric definition of patch counting entropy…
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…
We develop a new closed-form arithmetic and recursive formula for the partition function and a generalization of Andrews' smallest parts (spt) function. Using the inclusion-exclusion principle, we additionally develop a formula for the…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
We present upper and lower bounds to the relative entropy of entanglement of multi-party systems in terms of the bi-partite entanglements of formation and distillation and entropies of various subsystems. We point out implications of our…
We show that integer partitions, the fundamental building blocks in additive number theory, detect prime numbers in an unexpected way. Answering a question of Schneider, we show that the primes are the solutions to special equations in…
We present Euler-type recurrence relations for some partition functions. Some of our results provide new recurrences for the number of unrestricted partitions of $n$, denote by $p(n)$. Others establish recurrences for partition functions…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…