Related papers: Twenty Open Problems in Enumeration of Matchings: …
This document is an exposition of an assortment of open problems arising from the exact enumeration of (perfect) matchings of finite graphs. Roughly half have been solved at the time of this writing; see the document "Twenty Open Problems…
This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of…
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
The material of this work is aimed at mathematics educators, as well as math specialists with a keen interest in progressions. In this paper, we study the subject of arithmetic, geometric, mixed, and harmonic progressions or sequences. Some…
This paper presents fifteen problems about mapping class groups. It is an expanded and updated version of the author's preprint "Ten problems on the mapping class groups". The paper will appear in the book "Problems on Mapping Class Groups…
Enumeration of tilings is the mathematical study concerning the total number of coverings of regions by similar pieces without gaps or overlaps. Enumeration of tilings has become a vibrant subfield of combinatorics with connections and…
This paper gives an overview on and summarizes existing complexity and algorithmic results of some variants of the Stable Marriage and the Stable Roommates problems. The last section defines a list of stable matching problems mentioned in…
In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.
This habilitation thesis is intended to be a good introduction to enumeration, the problem of listing solutions. It focuses on the different ways of measuring complexity in enumeration, with a particular emphasis on my contributions to the…
This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one…
This is a survey of results in the enumeration of lattice paths.
This is an update on, and expansion of, our paper Open problems on $\beta\omega$ in the book Open Problems in Topology.
This is a structured compilation of some of my favourite open problems.
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…
This results in this paper have been merged with the result in arXiv:1002.3763v1 The authors would like to withdraw this version. Please see arXiv:1008.5356v1 for the merged version.
Matching, capturing allocation of items to unit-demand buyers, or tasks to workers, or pairs of collaborators, is a central problem in economics. Indeed, the growing prevalence of matching-based markets, many of which online in nature, has…
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.