@article{19433,
  abstract     = {An ordered r-matching is an r-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of r-dimensional orders. The theory of ordered 2-matchings is well developed and has connections and applications to extremal and enumerative combinatorics, probability and geometry. On the other hand, in the case  r≥3 much less is known, largely due to a lack of powerful bijective tools. Recently, Dudek, Grytczuk and Ruciński made some first steps towards a general theory of ordered r-matchings, and in this paper we substantially improve several of their results and introduce some new directions of study. Many intriguing open questions remain.},
  author       = {Anastos, Michael and Jin, Zhihan and Kwan, Matthew Alan and Sudakov, Benny},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Extremal, enumerative and probabilistic results on ordered hypergraph matchings}},
  doi          = {10.1017/fms.2024.144},
  volume       = {13},
  year         = {2025},
}