相关论文: Enumeration of Matchings: Problems and Progress
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…
An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a…
Job search through online matching engines nowadays are very prominent and beneficial to both job seekers and employers. But the solutions of traditional engines without understanding the semantic meanings of different resumes have not kept…
In 2000, I published a relatively comprehensive study of mappings between propositional satisfiability (SAT) and constraint satisfaction problems (CSPs) [Wal00]. I analysed four different mappings of SAT problems into CSPs, and two of CSPs…
These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
The paper described a generalized integrated glance to bin packing problems including a brief literature survey and some new problem formulations for the cases of multiset estimates of items. A new systemic viewpoint to bin packing problems…
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…
While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims…
We introduce a task consisting in matching a proof to a given mathematical statement. The task fits well within current research on Mathematical Information Retrieval and, more generally, mathematical article analysis (Mathematical…
Recent advances in reasoning with large language models (LLMs) have demonstrated strong performance on complex mathematical tasks, including combinatorial optimization. Techniques such as Chain-of-Thought and In-Context Learning have…
We consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a $2$-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an…
While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the…
The field of psychological sciences has been grappling with the replicability crisis. Various issues have been identified as potential sources of this problem. We bring to light a potential source that has largely been overlooked and…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in…