Related papers: Unique path partitions: Characterization and Congr…
We compute the congruence class modulo 16 of the number of unique path partitions of $n$ (as defined by Olsson), thus generalising previous results by Bessenrodt, Olsson and Sellers [Ann. Combin. 13 (2013), 591-602].
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…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…
We study the uniqueness properties of classical semiconjugations for analytic self-maps of the disk, by characterizing them as canonical solutions to certain functional equations. As a corollary, we obtain a complete description of all…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent…
In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our…
Recent work of Garvan, Sellers, Smoot, and others has made connections between infinite families of congruences for various partition functions. Here, we apply this approach to families of congruences for PED and POD partitions and find…
We consider $cp_{a,b,m}(n)$, the number of $(a,b,m)$-copartitions of $n$. We find many infinitelymany congruencesmodulo 2 and 6 for some particular value of $a$, $b$ and $m$.
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…
Extending the notion of $r$-(class) regular partitions, we define $(r_{1},...,r_{m})$-class regular partitions. A partition identity is presented and described by making use of the Glaisher correspondence.
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete…
We introduce the problem of partitioning 2D regions (usually convex regions) into mutually congruent pieces ('tiles').
We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by $m$, appearing fewer than $m$ times, or differing by less than $m$. We find results on their behavior and…
We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.
It is well known that the number of partitions into distinct even parts equals the number of $4$-regular partitions. In this paper we prove identities relating certain restricted partitions into distinct even parts with restricted…
We denote the number of partitions of $n$ wherein the even parts are distinct (and the odd parts are unrestricted) by $ped(n)$. In this paper, we will use generating function manipulations to obtain new congruences for $ped(n)$ modulo $24$.
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…