Related papers: Separable Integer Partition Classes
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
By jagged partitions we refer to an ordered collection of non-negative integers $(n_1,n_2,..., n_m)$ with $n_m\geq p$ for some positive integer $p$, further subject to some weakly decreasing conditions that prevent them for being genuine…
Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generalizations, the MacMahonesque functions, and prove there are…
Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible…
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…
We give an $n$-space generalized $q$-binomial theorem, and some new $q$ series identities that resemble the traditional $q$ series partition generating functions. These identities enumerate stepping stone weighted vector partitions.
Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
Recent results by Andrews and Merca on the number of even parts in all partitions of n into distinct parts, a(n), were derived via generating functions. This paper extends these results to the number of parts divisible by k in all the…
We study the enumeration problem of higher dimensional partitions, a natural generalisation of classical integer partitions. We show that their counting problem is equivalent to the enumeration of simpler classes of higher dimensional…
A scalar integer partition problem asks for a number of nonnegative integer solutions to a linear Diophantine equation with integer positive coefficients. The manuscript discusses an algorithm of derivation of linear relations involving the…
Categories of partial functions have become increasingly important principally because of their applications in theoretical computer science. In this note we prove that the category of partial bijections between sets as an…
The purpose of this paper is to present a collection of interesting generating functions for partitions which have connections to positive definite binary quadratic forms. In establishing our results we obtain some new Bailey pairs.
The number partition problem is a well-known problem, which is one of 21 Karp's NP-complete problems \cite{karp}. The partition function is a boolean function that is equivalent to the number partition problem with number range restricted.…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
We consider procedures of sampling parts from a random integer partition. We determine asymptotically the probabilty distribution of the randomly-selected part whenever the positive integer that is partitioned becomes large.
In this paper, we investigate the combinatorial properties of three classes of integer partitions: (1) $s$-modular partitions, a class consisting of partitions into parts with a number of occurrences (i.e., multiplicity) congruent to $0$ or…
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
We construct an evidently positive multiple series as a generating function for partitions satisfying the multiplicity condition in Schur's partition theorem. Refinements of the series when parts in the said partitions are classified…
In this article we study the "norm" of an integer partition, which we define to be the product of the parts. This partition-theoretic statistic has appeared here and there in the literature of the last century or so, and is at the heart of…