Related papers: Abaci structures of $(s,ms\pm1)$-core partitions

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…

We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a…

This paper investigates partitions which have neither parts nor hook lengths divisible by $p$, referred to as $p$-core $p'$-partitions. We show that the largest $p$-core $p'$-partition corresponds to the longest walk on a graph with…

Strict partitions are enumerated with respect to the weight, the number of parts, and the number of sequences of odd length. We write this trivariate generating function as a double sum $q$-series. Equipped with such a combinatorial set-up,…

We prove a product formula for the remaining cases of the weighted enumeration of self-complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removing the other half of the orbit changes the…

We develop the connection of Berg partitions with special substitution tilings of two tiles. We obtain a new proof that the number of Berg partitions with a fixed connectivity matrix is equal to half of the sum of its entries, \cite{S-W}.…

When a single core is scaled up to m cores occupying the same chip area and executing the same (parallelizable) task, achievable speedup is square-root m, power is reduced by square-root m and energy is reduced by m. Thus, many-core…

We consider a special type of integer partitions in which the parts of the form $p^aq^b$, for some relatively prime integers $p$ and $q$, are restricted by divisibility conditions. We investigate the problems of generating and encoding…

We present the construction of some kind of "convex core" for the product of two actions of a group on $\bbR$-trees. This geometric construction allows to generalize and unify the intersection number of two curves or of two measured…

In the light of a series of papers on moving vectors, we define and study core abaci of classical affine types for arbitrary charge. This greatly extends the concept of cores with charge zero, and make us being able to parameterize the…

We demonstrate the existence of multiple converging sequences in the ab initio no-core shell model. By examining the underlying theory of effective operators, we expose the physical foundations for the alternative pathways to convergence.…

The self assembly of core-corona discs interacting via anisotropic potentials is investigated using Monte Carlo computer simulations. A minimal interaction potential that incorporates anisotropy in a simple way is introduced. It consists in…

Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to extend one of these identities.

We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $\beta$. We prove that if $\beta$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $\beta$…

In this note, we investigate the detailed relationship between the orbifold partition counting and the (l-quotient, l-core) pair counting. We show that the orbifold partition counting is exactly the same as the (l-quotient, l-core) pair…

Given a sequence $S=(s_1,\dots,s_m) \in [0, 1]^m$, a block $B$ of $S$ is a subsequence $B=(s_i,s_{i+1},\dots,s_j)$. The size $b$ of a block $B$ is the sum of its elements. It is proved in [1] that for each positive integer $n$, there is a…

Let $A_{t,k}(n)$ denote the number of partition $k$-tuples of $n$ where each partition is $t$-core. In this paper, we establish formulas of $A_{t,k}(n)$ for some values of $t$ and $k$ by employing the method of modular forms, which extends…

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…

In this paper we refine a weighted partition identity of Alladi. We write explicit formulas of generating functions for the number of partitions grouped with respect to a partition statistic other than the norm. We tie our weighted results…

We incorporate explicit, non-perturbative treatment of spin-orbit coupling into ab initio auxiliary-field quantum Monte Carlo (AFQMC) calculations. The approach allows a general computational framework for molecular and bulk systems in…