Related papers: Schmidt-type theorems for partitions with uncounte…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
Herzog and Sch\"onheim conjectured that any nontrivial partition of a group into cosets must contain two cosets with the same index.
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 finite dimensional partition properties of the countable homogeneous dense local order. Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of…
We present an infinite family of recursive formulas that count binary integer partitions satisfying natural divisibility conditions and show that these counts are interrelated via partial sums. Moreover, we interpret the partitions we study…
Categories of partitions are combinatorial structures arising from the representation theory of certain compact quantum groups and are linked to classical diagram algebras such as the Temperley-Lieb algebra. In this paper, we present…
The PCT theorem is shown to be valid in quantum field theory formulated on noncommutative spacetime by exploiting the properties of the Wightman functions defined in such a set up.
The purpose of this paper is to study entanglement of quantum states by means of Schmidt decomposition. The notion of Schmidt information which characterizes the non-randomness of correlations between two observers that conduct measurements…
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…
One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…
We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…
In 1969, Andrews proved a theorem on partitions with difference conditions which generalises Schur's celebrated partition identity. In this paper, we generalise Andrews' theorem to overpartitions. The proof uses q-differential equations and…
We have recently showed that it is possible to deal with collections of indistinguishable elementary particles (in the context of quantum mechanics) in a set-theoretical framework by using hidden variables, in a sense. In the present paper…
We show a general scheme of Ramsey-type results for partitions of countable sets of finite functions, where "one piece is big" is interpreted in the language originating in creature forcing. The heart of our proofs follows Glazer's proof of…
We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been…
We establish a Pythagorean theorem for the absolute values of the blocks of a partitioned matrix. This leads to a series of remarkable operator inequalities.
We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so…