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We show that from a conjecture about forbidden 0\u20131 matrices it would follow that this bound is sharp for so-called doubly-grounded families. We also show that if the curves are required to be <jats:italic>x<\/jats:italic>-monotone, then the maximum number of tangencies is <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Theta (n\\log n)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u0398<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>log<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, which improves a result by Pach, Suk, and Treml. Finally, we also improve the best known bound on the number of tangencies between the members of a family of at most <jats:italic>t<\/jats:italic>-intersecting curves.<\/jats:p>","DOI":"10.1007\/s00493-023-00041-8","type":"journal-article","created":{"date-parts":[[2023,6,5]],"date-time":"2023-06-05T06:01:57Z","timestamp":1685944917000},"page":"939-952","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Number of Tangencies Between Two Families of Curves"],"prefix":"10.1007","volume":"43","author":[{"given":"Bal\u00e1zs","family":"Keszegh","sequence":"first","affiliation":[]},{"given":"D\u00f6m\u00f6t\u00f6r","family":"P\u00e1lv\u00f6lgyi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,5]]},"reference":[{"key":"41_CR1","doi-asserted-by":"publisher","unstructured":"Ackerman, E.: The Maximum Number of Tangencies Among Convex Regions with a Triangle-Free Intersection Graph, pp. 19\u201330. 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