{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T05:47:00Z","timestamp":1775800020889,"version":"3.50.1"},"reference-count":50,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T00:00:00Z","timestamp":1738886400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    This paper initiates the explicit study of face numbers of matroid polytopes and their computation. We prove that, for the large class of split matroid polytopes, their face numbers depend solely on the number of cyclic flats of each rank and size, together with information on the modular pairs of cyclic flats. We provide a formula which allows us to calculate\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325000021_inline1.png\"\/>\n                        <jats:tex-math>$f$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -vectors without the need of taking convex hulls or computing face lattices. We discuss the particular cases of sparse paving matroids and rank two matroids, which are of independent interest due to their appearances in other combinatorial and geometric settings.\n                  <\/jats:p>","DOI":"10.1017\/s0963548325000021","type":"journal-article","created":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T01:06:56Z","timestamp":1738890416000},"page":"528-544","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Face enumeration for split matroid polytopes"],"prefix":"10.1017","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5181-7932","authenticated-orcid":false,"given":"Luis","family":"Ferroni","sequence":"first","affiliation":[{"name":"Institute for Advanced Study"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3153-5211","authenticated-orcid":false,"given":"Benjamin","family":"Schr\u00f6ter","sequence":"additional","affiliation":[{"name":"KTH Royal Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,2,7]]},"reference":[{"key":"S0963548325000021_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2022.07.028"},{"key":"S0963548325000021_ref35","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-016-1709-8"},{"key":"S0963548325000021_ref14","doi-asserted-by":"publisher","DOI":"10.1006\/aima.2001.1991"},{"key":"S0963548325000021_ref9","doi-asserted-by":"crossref","first-page":"2373","DOI":"10.1109\/18.887851","article-title":"Upper bounds for constant-weight codes","volume":"46","author":"Agrell","year":"2000","journal-title":"IEEE Trans. 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