{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T18:33:54Z","timestamp":1768242834139,"version":"3.49.0"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Given\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100151_inline1.png\"\/>\n                        <jats:tex-math>$n$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    convex bodies in the Euclidean space\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100151_inline2.png\"\/>\n                        <jats:tex-math>$\\mathbb{R}^d$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , we can find their volume polynomial which is a homogeneous polynomial of degree\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100151_inline3.png\"\/>\n                        <jats:tex-math>$d$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    in\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100151_inline4.png\"\/>\n                        <jats:tex-math>$n$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    variables. We consider the set of homogeneous polynomials of degree\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100151_inline5.png\"\/>\n                        <jats:tex-math>$d$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    in\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100151_inline6.png\"\/>\n                        <jats:tex-math>$n$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    variables that can be represented as the volume polynomial of any such given convex bodies. This set is a subset of the set of Lorentzian polynomials. Using our knowledge of operations that preserve the Lorentzian property, we give a complete classification of the cases for\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100151_inline7.png\"\/>\n                        <jats:tex-math>$(n,d)$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    when the two sets are equal.\n                  <\/jats:p>","DOI":"10.1017\/s0963548325100151","type":"journal-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:02:46Z","timestamp":1758268966000},"page":"26-39","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Comparing the sets of volume polynomials and Lorentzian polynomials"],"prefix":"10.1017","volume":"35","author":[{"given":"Amelie","family":"Menges","sequence":"first","affiliation":[{"name":"Technische Universit\u00e4t Dortmund"}]}],"member":"56","published-online":{"date-parts":[[2025,9,19]]},"reference":[{"key":"S0963548325100151_ref15","first-page":"6","article-title":"Correspondences between convex geometry and complex geometry","volume":"1","author":"Lehmann","year":"2017","journal-title":"EPIGA"},{"key":"S0963548325100151_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01448930"},{"key":"S0963548325100151_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-804489-6.50001-X"},{"key":"S0963548325100151_ref19","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300001674"},{"key":"S0963548325100151_ref7","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2020.192.3.4"},{"key":"S0963548325100151_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-009-9147-5"},{"key":"S0963548325100151_ref9","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794278384"},{"key":"S0963548325100151_ref1","volume-title":"Selected Works. 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Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}