{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:48:34Z","timestamp":1776797314468,"version":"3.51.2"},"reference-count":16,"publisher":"American Mathematical Society (AMS)","issue":"291","license":[{"start":{"date-parts":[[2015,5,28]],"date-time":"2015-05-28T00:00:00Z","timestamp":1432771200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We discuss properties of root posets for finite crystallographic root systems, and show that these properties uniquely determine root posets for the noncrystallographic dihedral types and type\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H 3\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mn>3<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">H_3<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , while proving that there does not exist a poset satisfying all of the properties in type\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H 4\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mn>4<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">H_4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We do this by exhaustive computer searches for posets having these properties. We further give a realization of the poset of type\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H 3\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mn>3<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">H_3<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    as restricted roots of type\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper D 6\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>D<\/mml:mi>\n                            <mml:mn>6<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">D_6<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and conjecture a Hilbert polynomial for the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q comma t\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">q,t<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Catalan numbers for type\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H 4\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mn>4<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">H_4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-2014-02841-x","type":"journal-article","created":{"date-parts":[[2014,5,28]],"date-time":"2014-05-28T10:08:56Z","timestamp":1401271736000},"page":"485-503","source":"Crossref","is-referenced-by-count":6,"title":["On root posets for noncrystallographic root systems"],"prefix":"10.1090","volume":"84","author":[{"given":"Michael","family":"Cuntz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Stump","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2014,5,28]]},"reference":[{"key":"1","unstructured":"[Arm05] D. 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