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For integers <jats:inline-formula>\n              <jats:tex-math>$$r\\ge 2$$<\/jats:tex-math>\n            <\/jats:inline-formula>, <jats:inline-formula>\n              <jats:tex-math>$$t\\ge 1$$<\/jats:tex-math>\n            <\/jats:inline-formula>, <jats:inline-formula>\n              <jats:tex-math>$$\\mathcal {F}$$<\/jats:tex-math>\n            <\/jats:inline-formula> is called <jats:italic>r<\/jats:italic>-wise <jats:italic>t<\/jats:italic>-intersecting if any <jats:italic>r<\/jats:italic> of its members have at least <jats:italic>t<\/jats:italic> elements in common. The most natural construction of such a family is the full <jats:italic>t<\/jats:italic>-star, consisting of all <jats:italic>k<\/jats:italic>-sets containing a fixed <jats:italic>t<\/jats:italic>-set. In the case <jats:inline-formula>\n              <jats:tex-math>$$r=2$$<\/jats:tex-math>\n            <\/jats:inline-formula> the Exact Erd\u0151s-Ko-Rado Theorem shows that the full <jats:italic>t<\/jats:italic>-star is largest if <jats:inline-formula>\n              <jats:tex-math>$$n\\ge (t+1)(k-t+1)$$<\/jats:tex-math>\n            <\/jats:inline-formula>. In the present paper, we prove that for <jats:inline-formula>\n              <jats:tex-math>$$n\\ge (2.5t)^{1\/(r-1)}(k-t)+k$$<\/jats:tex-math>\n            <\/jats:inline-formula>, the full <jats:italic>t<\/jats:italic>-star is largest in case of <jats:inline-formula>\n              <jats:tex-math>$$r\\ge 3$$<\/jats:tex-math>\n            <\/jats:inline-formula>. Examples show that the exponent <jats:inline-formula>\n              <jats:tex-math>$$\\frac{1}{r-1}$$<\/jats:tex-math>\n            <\/jats:inline-formula> is best possible. This represents a considerable improvement on a recent result of Balogh and Linz.<\/jats:p>","DOI":"10.1007\/s00493-025-00166-y","type":"journal-article","created":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T07:04:59Z","timestamp":1754550299000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On r-wise t-intersecting Uniform Families"],"prefix":"10.1007","volume":"45","author":[{"given":"Peter","family":"Frankl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"166_CR1","first-page":"121","volume":"76","author":"R Ahlswede","year":"1996","unstructured":"Ahlswede, R., Khachatrian, L.H.: The complete non-trivial intersection theorem for systems of finite sets, J. 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