{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:07:48Z","timestamp":1753880868187,"version":"3.41.2"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p> In this paper, we investigate the root distribution of the Ehrhart polynomials of lattice polytopes. When the lattice polytope is reflexive, the roots of the Ehrhart polynomial distribute symmetrically with respect to the line [Formula: see text]. A special case of this distribution is when all the roots lie on this line. Our main concern is to find out which reflexive polytopes satisfy this special condition. Such lattice polytopes are called CL-polytopes. Another special case opposite to this is when all the roots are real. Such lattice polytopes are called real polytopes. The first topic of this paper is the Ehrhart polynomials of equatorial spheres, which are related to graded posets. We discuss the CL-ness of the equatorial Ehrhart polynomials for complete graded posets and zig-zag posets. The second topic is to investigate the relation of the root distribution of the Ehrhart polynomials of a reflexive polytope [Formula: see text] and its dual [Formula: see text]. We discuss the CL-ness and realness of [Formula: see text] and [Formula: see text] in pair, of dimensions up to 4. Throughout this paper, we investigate these problems by computer calculation. <\/jats:p>","DOI":"10.1142\/s0219198923400054","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T03:42:33Z","timestamp":1683258153000},"source":"Crossref","is-referenced-by-count":0,"title":["Some Computational Study of the Root Distribution of Ehrhart Polynomials"],"prefix":"10.1142","volume":"25","author":[{"given":"Masahiro","family":"Hachimori","sequence":"first","affiliation":[{"name":"Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan"}]},{"given":"Yumi","family":"Yamada","sequence":"additional","affiliation":[{"name":"Department of Policy and Planning Sciences, Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan"}]}],"member":"219","published-online":{"date-parts":[[2023,6,19]]},"reference":[{"key":"S0219198923400054BIB001","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1090\/conm\/374\/06897","volume-title":"Integer Points in Polyhedra \u2014 Geometry, Number Theory, Algebra, Optimization, Contemporary Mathematics","volume":"374","author":"Beck M.","year":"2005"},{"key":"S0219198923400054BIB002","series-title":"Undergraduate Texts in Mathematics","volume-title":"Computing the Continuous Discretely","author":"Beck M.","year":"2007"},{"key":"S0219198923400054BIB003","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s00454-008-9049-y","volume":"39","author":"Braun B.","year":"2008","journal-title":"Discrete Comput. 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