From aff743217e5a61e589729a9fb7f5fb0f56199676 Mon Sep 17 00:00:00 2001 From: patriciajklein <53194763+patriciajklein@users.noreply.github.com> Date: Tue, 31 Oct 2023 15:36:31 +0100 Subject: [PATCH] =?UTF-8?q?Changed=20Grobner=20to=20Gr=C3=B6bner?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Also Groebner to Gröbner --- .../MatrixSchubertConstructionsDOC.m2 | 30 +++++++++---------- MatrixSchubert/MatrixSchubertInvariantsDOC.m2 | 2 +- 2 files changed, 16 insertions(+), 16 deletions(-) diff --git a/MatrixSchubert/MatrixSchubertConstructionsDOC.m2 b/MatrixSchubert/MatrixSchubertConstructionsDOC.m2 index c8d7c9e3..6fd82930 100644 --- a/MatrixSchubert/MatrixSchubertConstructionsDOC.m2 +++ b/MatrixSchubert/MatrixSchubertConstructionsDOC.m2 @@ -16,17 +16,17 @@ doc /// Text @UL { {"[CV20] Aldo Conca and Matteo Varbaro, ", - HREF("https://arxiv.org/abs/1805.11923", EM "Square-free Grobner degenerations"), + HREF("https://arxiv.org/abs/1805.11923", EM "Square-free Gröbner degenerations"), ", Inventiones mathematicae, 221(3), pp.713-730."}, {"[Ful92] William Fulton, ", HREF("https://sites.math.washington.edu/~billey/classes/schubert.library/fulton.essential.set.pdf", EM "Flags, Schubert polynomials, degeneracy loci, and determinantal formulas"), ", Duke Math J. 65 (1992): 381-420."}, {"[KM05] Allen Knutson and Ezra Miller, ", - HREF("https://arxiv.org/abs/math/0110058", EM "Grobner geometry of Schubert polynomials"), + HREF("https://arxiv.org/abs/math/0110058", EM "Gröbner geometry of Schubert polynomials"), ", Annals of Mathematics (2005): 1245-1318."}, {"[KW21] Patricia Klein and Anna Weigandt, ", - HREF("https://arxiv.org/abs/2108.08370", EM "Bumpless pipe dreams encode Grobner geometry of Schubert polynomials"), + HREF("https://arxiv.org/abs/2108.08370", EM "Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials"), ", arxiv preprint 2108.08370."}, {"[PSW21] Oliver Pechenik, David Speyer, and Anna Weigandt, ", HREF("https://arxiv.org/abs/2111.10681", EM "Castelnuovo-Mumford regularity of matrix Schubert varieties"), @@ -71,10 +71,10 @@ doc /// EM "Flags, Schubert polynomials, degeneracy loci, and determinantal formulas"), ", Duke Math J. 65 (1992): 381-420."}, {"[HPW22] Zachary Hamaker, Oliver Pechenik, and Anna Weigandt, ", - HREF("https://arxiv.org/abs/2003.13719", EM "Grobner geometry of Schubert polynomials through ice"), + HREF("https://arxiv.org/abs/2003.13719", EM "Gröbner geometry of Schubert polynomials through ice"), ", Advances in Mathematics 398 (2022): 108228."}, {"[KM05] Allen Knutson and Ezra Miller, ", - HREF("https://arxiv.org/abs/math/0110058", EM "Grobner geometry of Schubert polynomials"), + HREF("https://arxiv.org/abs/math/0110058", EM "Gröbner geometry of Schubert polynomials"), ", Annals of Mathematics (2005): 1245-1318."}, {"[PSW21] Oliver Pechenik, David Speyer, and Anna Weigandt, ", HREF("https://arxiv.org/abs/2111.10681", EM "Castelnuovo-Mumford regularity of matrix Schubert varieties"), @@ -159,7 +159,7 @@ doc /// Text @UL { {"[CV20] Aldo Conca and Matteo Varbaro, ", - HREF("https://arxiv.org/abs/1805.11923", EM "Square-free Grobner degenerations"), + HREF("https://arxiv.org/abs/1805.11923", EM "Square-free Gröbner degenerations"), ", Inventiones mathematicae, 221(3), pp.713-730."}, {"[Wei17] Anna Weigandt, ", HREF("https://arxiv.org/abs/1708.07236", EM "Prism tableaux for alternating sign matrix varieties"), @@ -267,8 +267,8 @@ doc /// Description Text By work of Knutson and Miller [KM05], Weigandt [Wei17], and Knutson [Knu09] - the Fulton generators of an ASM ideal form a Groebner basis with respect to any antidiagonal term order. - However, Groebner bases for ASM ideals with respect to other term orders, including diagonal ones, + the Fulton generators of an ASM ideal form a Gröbner basis with respect to any antidiagonal term order. + However, Gröbner bases for ASM ideals with respect to other term orders, including diagonal ones, remain largely mysterious. Text @UL { @@ -276,10 +276,10 @@ doc /// HREF("https://projecteuclid.org/journals/experimental-mathematics/volume-2/issue-4/RC-graphs-and-Schubert-polynomials/em/1048516036.full", EM "RC-graphs and Schubert polynomials"), ", Experiment. Math.2(1993), no.4, 257–269."}, {"[CV20] Aldo Conca and Matteo Varbaro, ", - HREF("https://arxiv.org/abs/1805.11923", EM "Square-free Grobner degenerations"), + HREF("https://arxiv.org/abs/1805.11923", EM "Square-free Gröbner degenerations"), ", Inventiones mathematicae, 221(3), pp.713-730."}, {"[HPW22] Zachary Hamaker, Oliver Pechenik, and Anna Weigandt, ", - HREF("https://arxiv.org/abs/2003.13719", EM "Grobner geometry of Schubert polynomials through ice"), + HREF("https://arxiv.org/abs/2003.13719", EM "Gröbner geometry of Schubert polynomials through ice"), ", Advances in Mathematics 398 (2022): 108228."}, {"[Kle23] Patricia Klein, ", HREF("https://arxiv.org/abs/2008.01717", EM "Diagonal degenerations of matrix Schubert varieties"), @@ -294,7 +294,7 @@ doc /// HREF("https://arxiv.org/abs/math/0502144", EM "Gröbner geometry of vertex decompositions and of flagged tableaux"), ", J. Reine Angew. Math.630(2009), 1-31."}, {"[KW21] Patricia Klein and Anna Weigandt, ", - HREF("https://arxiv.org/abs/2108.08370", EM "Bumpless pipe dreams encode Grobner geometry of Schubert polynomials"), + HREF("https://arxiv.org/abs/2108.08370", EM "Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials"), ", arxiv preprint 2108.08370."}, {"[Wei17] Anna Weigandt, ", HREF("https://arxiv.org/abs/1708.07236", EM "Prism tableaux for alternating sign matrix varieties"), @@ -302,7 +302,7 @@ doc /// }@ Text Given a permutation or a partial ASM, one may compute its antidiagonal initial ideal. - By [KM05] and [Wei17] or [Knu09], the Fulton generators form a Groebner basis for any ASM ideal with respect to + By [KM05] and [Wei17] or [Knu09], the Fulton generators form a Gröbner basis for any ASM ideal with respect to any antidiagonal term order. Example w = {2,4,5,1,3}; @@ -376,16 +376,16 @@ doc /// HREF("https://arxiv.org/abs/2108.10115", EM "Radical generic initial ideals"), ", Vietnam J. Math.50(2022), no.3, 807–827."}, {"[HPW22] Zachary Hamaker, Oliver Pechenik, and Anna Weigandt, ", - HREF("https://arxiv.org/abs/2003.13719", EM "Grobner geometry of Schubert polynomials through ice"), + HREF("https://arxiv.org/abs/2003.13719", EM "Gröbner geometry of Schubert polynomials through ice"), ", Advances in Mathematics 398 (2022): 108228."}, {"[Kle23] Patricia Klein, ", HREF("https://arxiv.org/abs/2008.01717", EM "Diagonal degenerations of matrix Schubert varieties"), ", Algebraic Combinatorics 6 (2023) no. 4, 1073-1094."}, {"[KW21] Patricia Klein and Anna Weigandt, ", - HREF("https://arxiv.org/abs/2108.08370", EM "Bumpless pipe dreams encode Grobner geometry of Schubert polynomials"), + HREF("https://arxiv.org/abs/2108.08370", EM "Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials"), ", arxiv preprint 2108.08370."}, {"[KM05] Allen Knutson and Ezra Miller, ", - HREF("https://arxiv.org/abs/math/0110058", EM "Grobner geometry of Schubert polynomials"), + HREF("https://arxiv.org/abs/math/0110058", EM "Gröbner geometry of Schubert polynomials"), ", Annals of Mathematics (2005): 1245-1318."}, {"[KMY09] Allen Knutson, Ezra Miller, and Alexander Yong ", HREF("https://arxiv.org/abs/math/0502144", EM "Gröbner geometry of vertex decompositions and of flagged tableaux"), diff --git a/MatrixSchubert/MatrixSchubertInvariantsDOC.m2 b/MatrixSchubert/MatrixSchubertInvariantsDOC.m2 index be5207ca..43bec1ab 100644 --- a/MatrixSchubert/MatrixSchubertInvariantsDOC.m2 +++ b/MatrixSchubert/MatrixSchubertInvariantsDOC.m2 @@ -23,7 +23,7 @@ doc /// In the case of a partial permutation, computes the regularity using the antidiagonal initial ideal, a valid strategy in light of @UL { - {"Aldo Conca and Matteo Varbaro, ", EM "Square-free Groebner degenerations, ", arXiv "1805.11923", ", ", "Invent. Math. 221 (2020), no. 3, 713–730."} + {"Aldo Conca and Matteo Varbaro, ", EM "Square-free Gröbner degenerations, ", arXiv "1805.11923", ", ", "Invent. Math. 221 (2020), no. 3, 713–730."} }@ Example