{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:59:51Z","timestamp":1776790791682,"version":"3.51.2"},"reference-count":33,"publisher":"American Mathematical Society (AMS)","issue":"267","license":[{"start":{"date-parts":[[2010,2,25]],"date-time":"2010-02-25T00:00:00Z","timestamp":1267056000000},"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                    Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of the Schubert problem of 3-planes in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper C Superscript 8\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">C<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>8<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {C}^8<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    meeting 15 fixed 5-planes non-trivially is the full symmetric group\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S 6006\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>6006<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">S_{6006}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-09-02239-x","type":"journal-article","created":{"date-parts":[[2009,4,27]],"date-time":"2009-04-27T13:47:33Z","timestamp":1240840053000},"page":"1749-1765","source":"Crossref","is-referenced-by-count":24,"title":["Galois groups of Schubert problems via homotopy computation"],"prefix":"10.1090","volume":"78","author":[{"given":"Anton","family":"Leykin","sequence":"first","affiliation":[]},{"given":"Frank","family":"Sottile","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,2,25]]},"reference":[{"key":"1","unstructured":"Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler, Bertini: Software for numerical algebraic geometry, Available at http:\/\/ www. nd. edu\/ \u02dcsommese\/ bertini."},{"key":"2","unstructured":"Daniel J. Bates, Andrew J. Peterson, Chrisand Sommese, and Charles W. Wampler, Numerical computation of the genus of an irreducible curve within an algebraic set, 2007."},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/978-0-387-75155-9_3","article-title":"Intersections of Schubert varieties and other permutation array schemes","author":"Billey, Sara","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387751542"},{"key":"4","isbn-type":"print","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/BFb0008458","article-title":"Pole assignment by output feedback","author":"Byrnes, C. I.","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/3540516050"},{"key":"5","series-title":"London Mathematical Society Student Texts","isbn-type":"print","volume-title":"Young tableaux","volume":"35","author":"Fulton, William","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/0521561442"},{"key":"6","unstructured":"The GAP Group, GAP \u2013 Groups, Algorithms, and Programming, Version 4.4.9, 2006."},{"key":"7","isbn-type":"print","first-page":"43","article-title":"polymake: a framework for analyzing convex polytopes","author":"Gawrilow, Ewgenij","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/3764363517"},{"issue":"4","key":"8","first-page":"685","article-title":"Galois groups of enumerative problems","volume":"46","author":"Harris, Joe","year":"1979","journal-title":"Duke Math. 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