Related papers: Weighted File Placements on Singleton Boards

In 1996, Michael Stiebitz proved that if $G$ is a simple graph with $\delta(G)\geq s+t+1$ and $s,t\in \mathbb{Z}_{\geq 0}$, then $V(G)$ can be partitioned into two sets $A$ and $B$ such that $\delta(G[A])\geq s$ and $\delta(G[B])\geq t$. In…

A weighted bicolored plane tree is a bicolored plane tree whose edges are endowed with positive integral weights. The degree of a vertex is defined as the sum of the weights of the edges incident to this vertex. Using the theory of dessins…

Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…

Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of low-rank tensor factorization (LRTF) has been applied for the recovery of a low dimensional subspace from high dimensional…

We study the weighted partition function for lozenge tilings, with weights given by multivariate rational functions originally defined by Morales, Pak and Panova (2019) in the context of the factorial Schur functions. We prove that this…

All ten symmetry classes of plane partitions that fit in a given box are known to be enumerated by simple product formulas, but there is still no unified proof for all of them. Progress towards this goal can be made by establishing…

Let $(X,T)$ and $(Y,S)$ be two subshifts so that $Y$ is a factor of $X$. For any asymptotically sub-additive potential $\Phi$ on $X$ and $\ba=(a,b)\in\R^2$ with $a>0$, $b\geq 0$, we introduce the notions of $\ba$-weighted topological…

Jaramillo Puentes et al. give a Grothendieck-Witt valued floor-diagram formula for rational curves in smooth toric del Pezzo surfaces with simple and quadratic double point conditions. We study its dependence on the choice of merge…

A rook placement is a subset of a root system consisting of positive roots with pairwise non-positive inner products. To each rook placement in a root system one can assign the coadjoint orbit of the Borel subgroup of a reductive algebraic…

In this paper, we consider plane partitions $\text{PP}(\lambda; m)$ of a given shape $\lambda$, with entries at most $m$. We prove that the distributions of two statistics on $\text{PP}(\lambda; m)$ coincide: one is the number of rows…

File systems must allocate space for files without knowing what will be added or removed in the future. Over the life of a file system, this may cause suboptimal file placement decisions that eventually lead to slower performance, or aging.…

The notion of the spt-crank of a vector partition, or an $S$-partition, was introduced by Andrews, Garvan and Liang. Let $N_S(m,n)$ denote the number of $S$-partitions of $n$ with spt-crank $m$. Andrews, Dyson and Rhoades conjectured that…

For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals of the coefficients in the factorizations of semigroup elements. This work generalizes many…

In this work, we consider the problem of placing replicas in a data center or storage area network, represented as a digraph, so as to lexico-minimize a previously proposed reliability measure which minimizes the impact of all failure…

We prove the 4-uniform Erd\H{o}s Matching Conjecture for every matching number $s\ge 6961$. The proof has two parts. First, building on ideas from Frankl--R\"odl--Ruci\'nski, we formulate a general finite-board criterion for the $r$-uniform…

We propose a unified theory of generalized weights for linear codes endowed with an arbitrary distance. Instead of relying on supports or anticodes, the weights of a code are defined via the intersections of the code with a chosen family of…

We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations of simplicial affine semigroups and numerical semigroups.…

We consider the problem of allocating $m$ indivisible items to a set of $n$ heterogeneous agents, aiming at computing a proportional allocation by introducing subsidy (money). It has been shown by Wu et al. (WINE 2023) that when agents are…

We study random packings of frictionless particles at T=0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing…

We study the asymptotic growth rate of the label size of high-degree vertices in weighted recursive graphs (WRG) when the weights are i.i.d. almost surely bounded random variables, and as a result confirm a conjecture by Lodewijks and…