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The MatrixSchubert
package for Macaulay2
Ayah Almousa, Sean Grate, Daoji Huang, Patricia Klein, Adam LaClair, Yuyuan Luo and Joseph McDonough |
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Vol. 15 (2025), 41–55
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Abstract |
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We introduce the MatrixSchubert package for the computer algebra system Macaulay2. This package has tools to construct and study matrix Schubert varieties and alternating sign matrix (ASM) varieties. The package also introduces tools for quickly computing homological invariants of such varieties, finding the components of an ASM variety, and checking if a union of matrix Schubert varieties is an ASM variety. |
Keywords
matrix Schubert varieties, alternating sign matrices, pipe
dreams, Grothendieck polynomials, Castelnuovo–Mumford
regularity, Schubert calculus, Schubert polynomial
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Mathematical Subject Classification
Primary: 05E14, 05E40, 13C70, 13P10, 14M12
Secondary: 05A05, 13C15, 14M15, 14N15
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Supplementary material |
Milestones
Received: 19 December 2023
Revised: 17 January 2025
Accepted: 19 March 2025
Published: 20 May 2025
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Authors |
| Ayah Almousa | |
| Department of Mathematics University of South Carolina LeConte College Columbia, SC United States |
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| Sean Grate | |
| Department of Mathematics and
Statistics Auburn University Auburn, AL United States |
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| Daoji Huang | |
| Institute for Advanced Study Princeton, NJ United States |
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| Patricia Klein | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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| Adam LaClair | |
| Department of Mathematics Purdue University West Lafayette, IN United States |
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| Yuyuan Luo | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| Joseph McDonough | |
| School of Mathematics University of Minnesota – Twin Cities Minneapolis, MN United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
