Related papers: Unlimited parity alternating partitions
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
For quantum field theories with global symmetry, we can study the behavior of the partition function with the background gauge field to diagnose different quantum phases. For the case of discrete symmetries, we find that the…
The paper introduce a new type of partitions where the largest part appears exactly once, and the remaining parts constitute a partition of that largest part. We derive the generating function associated with these partitions and…
This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising…
The convergence of simultaneous and marginal predictive classifiers under partition exchangeability in supervised classification is obtained. The result shows the asymptotic convergence of these classifiers under infinite amount of training…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts and then measure the joint…
We find a countable partition $P$ on\textbf{} a Lebesgue space, labeled $\{1,2,3...$\}, for any non-periodic measure preserving transformation $T$ such that $P$ generates $T$ and for the $T,P$ process, if you see an $n$ on time -1 then you…
Extending the rigorous presentation of the classical umbral calculus given by Rota and Taylor in 1994, the so-called partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among…
Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow…
Considering Schur positivity of differences of plethysms of homogeneous symmetric functions, we introduce a new relation on integer partitions. This relation is conjectured to be a partial order, with its restriction to one part partitions…
A preferential arrangement of a finite set is an ordered partition. Associated with each such ordered partition is a chain of subsets or blocks endowed with a linear order. The chain may be split into sections by the introduction of a…
We present a new set of inseparabilty inequalities to detect entanglement in $N$-spin states. These are based on negative partial transposition and involve collective spin-spin correlations of any two partitions of the entire system. They…
The aim of this paper is to present the construction of exceptional Laguerre polynomials in a systematic way, and to provide new asymptotic results on the location of the zeros. To describe the exceptional Laguerre polynomials we associate…
E158 in the Enestrom index. Translation of the Latin original "Observationes analyticae variae de combinationibus" (1741). This paper introduces the problem of partitions, or partitio numerorum (the partition of integers). In the first part…
In a previous paper: A. Paszkiewicz, T. Sobieszek, Additive Entropies of Partitions, we have given a description of additive partition entropies that is real functions $I$ on the set of finite partitions that are additive on stochastically…
In this article, we provide partition-theoretic interpretations for some new truncated pentagonal number theorem and identities of Gauss. Also, we deduce few inequalities for some partition functions.
One of the interesting features about field theories in odd dimensions is the induction of parity violating terms and well-defined {\em finite} topological actions via quantum loops if a fermion mass term is originally present and…
In a 2022 paper, Dawsey, Just and the present author prove that the set of integer partitions, taken as a monoid under a partition multiplication operation I defined in my Ph.D. work, is isomorphic to the positive integers as a monoid under…
This paper considers three different partition relations from partition calculus, two of which are pair relations and one of which is a triple relation. An examination of the first partition relation and the ramification argument used to…