Skip to content

Commit

Permalink
Changed Grobner to Gröbner
Browse files Browse the repository at this point in the history 
Also Groebner to Gröbner
  • Loading branch information
@patriciajklein
patriciajklein committed Oct 31, 2023
1 parent 928447c commit aff7432
Show file tree
Hide file tree
Showing 2 changed files with 16 additions and 16 deletions.
30 changes: 15 additions & 15 deletions MatrixSchubert/MatrixSchubertConstructionsDOC.m2
View file
Original file line number Diff line number Diff line change
Expand Up @@ -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"),
Expand Down Expand Up @@ -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"),
Expand Down Expand Up @@ -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"),
Expand Down Expand Up @@ -267,19 +267,19 @@ 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 {
{"[BB93] Nantel Bergeron and Sara Billey, ",
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"),
Expand All @@ -294,15 +294,15 @@ 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"),
", arXiv preprint 1708.07236."}
}@
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};
Expand Down Expand Up @@ -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"),
Expand Down
2 changes: 1 addition & 1 deletion MatrixSchubert/MatrixSchubertInvariantsDOC.m2
View file
Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand Down

0 comments on commit aff7432

Please sign in to comment.