{"id":3177,"global_id":"colleges.claremont.edu\/ccms?id=3177","global_id_lineage":["colleges.claremont.edu\/ccms?id=3177"],"author":"73","status":"publish","date":"2023-09-07 22:56:25","date_utc":"2023-09-08 05:56:25","modified":"2023-11-08 23:01:58","modified_utc":"2023-11-09 07:01:58","url":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-max-hlavacek-pomona-college\/","rest_url":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/tribe\/events\/v1\/events\/3177","title":"f^*-vectors of lattice polytopes (Max Hlavacek, Pomona College)","description":"<p>The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. The f^* -vector of P, introduced by Felix Breuer in 2012, is the vector of coefficients of the Ehrhart polynomial with respect to the binomial coefficient basis . Similarly to h and h^* -vectors, the f^* -vector of P coincides with the f-vector (counting faces of every dimension) of its unimodular triangulations (if they exist). We give several inequalities that hold among the coefficients of f^*-vectors of polytopes. These inequalities resemble striking similarities with existing inequalities for the coefficients of f-vectors of simplicial polytopes. Even though f^* -vectors of polytopes are not always unimodal, we describe several families of polytopes that carry the unimodality property.<\/p>","excerpt":"","slug":"antc-seminar-max-hlavacek-pomona-college","image":false,"all_day":false,"start_date":"2023-11-14 12:15:00","start_date_details":{"year":"2023","month":"11","day":"14","hour":"12","minutes":"15","seconds":"00"},"end_date":"2023-11-14 13:10:00","end_date_details":{"year":"2023","month":"11","day":"14","hour":"13","minutes":"10","seconds":"00"},"utc_start_date":"2023-11-14 20:15:00","utc_start_date_details":{"year":"2023","month":"11","day":"14","hour":"20","minutes":"15","seconds":"00"},"utc_end_date":"2023-11-14 21:10:00","utc_end_date_details":{"year":"2023","month":"11","day":"14","hour":"21","minutes":"10","seconds":"00"},"timezone":"America\/Los_Angeles","timezone_abbr":"PST","cost":"","cost_details":{"currency_symbol":"","currency_code":"","currency_position":"","values":[]},"website":"","show_map":true,"show_map_link":true,"hide_from_listings":false,"sticky":false,"featured":false,"categories":[{"name":"Algebra \/ Number Theory \/ Combinatorics Seminar","slug":"antc-seminar","term_group":0,"term_taxonomy_id":13,"taxonomy":"tribe_events_cat","description":"","parent":0,"count":171,"filter":"raw","term_order":"0","id":13,"urls":{"self":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/tribe\/events\/v1\/categories\/13","collection":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/tribe\/events\/v1\/categories"}}],"tags":[],"venue":{"id":3147,"author":"73","status":"publish","date":"2023-08-24 09:14:27","date_utc":"2023-08-24 16:14:27","modified":"2023-08-28 09:35:16","modified_utc":"2023-08-28 16:35:16","url":"https:\/\/colleges.claremont.edu\/ccms\/venue\/roberst-north-102-cmc\/","venue":"Roberts North 102, CMC","slug":"roberst-north-102-cmc","json_ld":{"@type":"Place","name":"Roberts North 102, CMC","description":"","url":"https:\/\/colleges.claremont.edu\/ccms\/venue\/roberst-north-102-cmc\/","address":{"@type":"PostalAddress"},"telephone":"","sameAs":""},"show_map":true,"show_map_link":true,"global_id":"colleges.claremont.edu\/ccms?id=3147","global_id_lineage":["colleges.claremont.edu\/ccms?id=3147"]},"organizer":[{"id":426,"author":"73","status":"publish","date":"2018-08-17 08:08:12","date_utc":"2018-08-17 15:08:12","modified":"2018-08-17 08:08:12","modified_utc":"2018-08-17 15:08:12","url":"https:\/\/colleges.claremont.edu\/ccms\/organizer\/lenny-fukshansky-4\/","organizer":"Lenny Fukshansky","slug":"lenny-fukshansky-4","json_ld":{"@type":"Person","name":"Lenny Fukshansky","description":"","url":"","telephone":"","email":"","sameAs":""},"global_id":"colleges.claremont.edu\/ccms?id=426","global_id_lineage":["colleges.claremont.edu\/ccms?id=426"]},{"id":433,"author":"73","status":"publish","date":"2018-08-08 15:52:55","date_utc":"2018-08-08 22:52:55","modified":"2018-08-08 15:52:55","modified_utc":"2018-08-08 22:52:55","url":"https:\/\/colleges.claremont.edu\/ccms\/organizer\/gizem-karaali-2\/","organizer":"Gizem Karaali","slug":"gizem-karaali-2","json_ld":{"@type":"Person","name":"Gizem Karaali","description":"","url":"","telephone":"","email":"","sameAs":""},"global_id":"colleges.claremont.edu\/ccms?id=433","global_id_lineage":["colleges.claremont.edu\/ccms?id=433"]}],"custom_fields":[],"json_ld":{"@context":"http:\/\/schema.org","@type":"Event","name":"f^*-vectors of lattice polytopes (Max Hlavacek, Pomona College)","description":"&lt;p&gt;The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. 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