article published yes Michael Anastos author 0b2a4358-bb35-11ec-b7b9-e3279b593dbb Zhihan Jin author Matthew Alan Kwan author 5fca0887-a1db-11eb-95d1-ca9d5e0453b30000-0002-4003-7567 Benny Sudakov author MaKw department IST-BRIDGE: International postdoctoral program project Randomness and structure in combinatorics project 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. https://research-explorer.ista.ac.at/download/19433/19468/2025_ForumMathSigma_Anastos.pdf application/pdfno Cambridge University Press2025 eng 2050-5094 2308.12268 00144442920000110.1017/fms.2024.144 13 M. Anastos, Z. Jin, M. A. Kwan, and B. Sudakov, “Extremal, enumerative and probabilistic results on ordered hypergraph matchings,” <i>Forum of Mathematics, Sigma</i>, vol. 13. Cambridge University Press, 2025. M. Anastos, Z. Jin, M.A. Kwan, B. Sudakov, Forum of Mathematics, Sigma 13 (2025). Anastos, M., Jin, Z., Kwan, M. A., &#38; Sudakov, B. (2025). Extremal, enumerative and probabilistic results on ordered hypergraph matchings. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href="https://doi.org/10.1017/fms.2024.144">https://doi.org/10.1017/fms.2024.144</a> Anastos, Michael, et al. “Extremal, Enumerative and Probabilistic Results on Ordered Hypergraph Matchings.” <i>Forum of Mathematics, Sigma</i>, vol. 13, e55, Cambridge University Press, 2025, doi:<a href="https://doi.org/10.1017/fms.2024.144">10.1017/fms.2024.144</a>. Anastos M, Jin Z, Kwan MA, Sudakov B. 2025. Extremal, enumerative and probabilistic results on ordered hypergraph matchings. Forum of Mathematics, Sigma. 13, e55. Anastos M, Jin Z, Kwan MA, Sudakov B. Extremal, enumerative and probabilistic results on ordered hypergraph matchings. <i>Forum of Mathematics, Sigma</i>. 2025;13. doi:<a href="https://doi.org/10.1017/fms.2024.144">10.1017/fms.2024.144</a> Anastos, Michael, Zhihan Jin, Matthew Alan Kwan, and Benny Sudakov. “Extremal, Enumerative and Probabilistic Results on Ordered Hypergraph Matchings.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2025. <a href="https://doi.org/10.1017/fms.2024.144">https://doi.org/10.1017/fms.2024.144</a>. 194332025-03-20T12:59:14Z2025-09-30T11:18:57Z