相关论文: Mullineux map: $d$-balanced partitions and $d$-run…

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

The Mondrian problem consists of dissecting a square of side length $n\in \NN$ into non-congruent rectangles with natural length sides such that the difference $d(n)$ between the largest and the smallest areas of the rectangles partitioning…

A Robinson space is a dissimilarity space $(X,d)$ (i.e., a set $X$ of size $n$ and a dissimilarity $d$ on $X$) for which there exists a total order $<$ on $X$ such that $x<y<z$ implies that $d(x,z)\ge \max\{ d(x,y), d(y,z)\}$. Recognizing…

A metric space $\mathrm{M}=(M,\de)$ is {\em indivisible} if for every colouring $\chi: M\to 2$ there exists $i\in 2$ and a copy $\mathrm{N}=(N, \de)$ of $\mathrm{M}$ in $\mathrm{M}$ so that $\chi(x)=i$ for all $x\in N$. The metric space…

We give new lower bounds for $M(n,d)$, for various positive integers $n$ and $d$ with $n>d$, where $M(n,d)$ is the largest number of permutations on $n$ symbols with pairwise Hamming distance at least $d$. Large sets of permutations on $n$…

Let $T$ be a tree on $n$ vertices and let $L_q^T$ be the $q$-analogue of its Laplacian. For a partition $\lambda \vdash n$, let the normalized immanant of $L_q^T$ indexed by $\lambda$ be denoted as $d_{\lambda}(L_q^T)$. A string of…

We prove that for any partition $(\lambda_1,...,\lambda_{d^2})$ of size $\ell d$ there exists $k\ge 1$ such that the tensor square of the irreducible representation of the symmetric group $S_{k\ell d}$ with respect to the rectangular…

By exploiting relationships between the values taken by ordinary characters of symmetric groups we prove two theorems in the modular representation theory of the symmetric group. 1. The decomposition matrices of symmetric groups in odd…

We study the existence of unitriangular basic sets for the symmetric group which behave nicely with respect to the Mullineux involution. Such sets give a natural labelling for the modular irreducible representations. We show that, for any…

Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and…

The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…

We develop structural insights into the Littlewood-Richardson graph, whose number of vertices equals the Littlewood-Richardson coefficient c({\lambda},{\mu},{\nu}) for given partitions {\lambda}, {\mu}, and {\nu}. This graph was first…

A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…

We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is $D$-equivalent to an ultrametric, where $D\in (2,\infty)$ is a prescribed target…

Given an integer partition $\la=(\la_1, ..., \la_\ell)$ and an integer k, denote by $\la^{(k)}$ the sequence of length $\ell$ obtained by reordering the values $|\la_i-k|$ in non-increasing order. If $\la$ dominates $\mu$ and has the same…

The Dulmage-Mendelsohn decomposition is a classical canonical decomposition in matching theory applicable for bipartite graphs, and is famous not only for its application in the field of matrix computation, but also for providing a…

Several Riemannian metrics and families of Riemannian metrics were defined on the manifold of Symmetric Positive Definite (SPD) matrices. Firstly, we formalize a common general process to define families of metrics: the principle of…

The problem of classifying modules over a tame algebra A reduces to a block matrix problem of tame type whose indecomposable canonical matrices are zero- or one-parameter. Respectively, the set of nonisomorphic indecomposable modules of…

We establish a structure theorem for rational maps $f:\overline{\mathbb{C}}\to\overline{\mathbb{C}}$: the pullback metric $f^{*}{\rm d}s_{0}^{2}$ of the standard metric ${\rm d}s_{0}^{2}$ admits a canonical decomposition into finitely many…

We consider a type of distance-regular graph $\Gamma=(X, \mathcal R)$ called a bilinear forms graph. We assume that the diameter $D$ of $\Gamma$ is at least $3$. Fix adjacent vertices $x,y \in X$. In our first main result, we introduce an…