Related papers: A generalization of Kakutani's splitting procedure
The challenges of examining random partitions of space are a significant class of problems in the theory of geometric transformations. Richard Miles calculated moments of areas and perimeters of any order (including expectation) of the…
The divided cell algorithm was introduced by Delone in 1947 to calculate the inhomogeneous minima of binary quadratic forms and developed further by E. S. Barnes and H. P. F. Swinnerton-Dyer in the 1950s. We show how advances of the past…
Recent works at the interface of algebraic combinatorics, algebraic geometry, number theory, and topology have provided new integer-valued invariants on integer partitions. It is natural to consider the distribution of partitions when…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
A Kakutani-von Neumann map is the push-forward of the group rotation (Z_2,+1) to a unit simplex via an appropriate topological quotient. The usual quotient towards the unit interval is given by the base 2 expansion of real numbers, which in…
In the limit where partons become collinear to each other, scattering amplitudes factorize into a product of universal, process-independent building blocks and scattering amplitudes involving fewer partons. We compute these universal…
We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…
We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Fa\`a di Bruno coefficients. Besides attempting to summarize what is…
The distribution of a given sequence in the set of all sequences with n ones and m = M - n zeros are found by relating the problem to the partitions of a natural number in m natural summands, taking into account the order. The formulas…
Given a subset of size $k$ of a very large universe a randomized way to find this subset could consist of deleting half of the universe and then searching the remaining part. With a probability of $2^{-k}$ one will succeed. By probability…
In this paper, we give a new completion for quasi-uniform spaces which generalizes the completion theories of Doitchinov [8] and Stoltenberg [20]. The presented completion theory is very well-behaved and extends the completion theory of…
In his foundational paper [ICM 1983, Warzaw], Ma\~n\'e suggested that some aspects of the Oseledets splitting could be improved if one worked under C1-generic conditions. He announced some powerful theorems, and suggested some lines to…
We summarize recent developments in understanding the concept of generalized parton distributions (GPDs), its relation to nucleon structure, and its application to high-Q2 electroproduction processes. Following a brief review of QCD…
Motivated by the Nekrasov-Okounkov formula on hook lengths, the first author conjectured that the Plancherel average of the $2k$-th power sum of hook lengths of partitions with size $n$ is always a polynomial of $n$ for any $k\in…
The basic properties of generalized parton distributions (GPDs) and some recent applications of GPDs are discussed
The famous partition theorem of Euler states that partitions of $n$ into distinct parts are equinumerous with partitions of $n$ into odd parts. Another famous partition theorem due to MacMahon states that the number of partitions of $n$…
This paper presents a new `partitional' approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set…
The concept of full points of abstract unitals has been introduced by Korchm\'aros, Siciliano and Sz\H{o}nyi as a tool for the study of projective embeddings of abstract unitals. In this paper we give a more detailed description of the…
The concepts of Generalized Parton Distributions (GPD) are reviewed in an introductory and phenomenological fashion. These distributions provide a rich and unifying picture of the nucleon structure. Their physical meaning is discussed. The…