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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.18030 |
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| _version_ | 1866915921504763904 |
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| author | Bingham, Aram Castellano, Beth Anne Hadaway, Kimberly P. Hodges, Reuven Ma, Yichen Moon, Alex Salois, Kyle |
| author_facet | Bingham, Aram Castellano, Beth Anne Hadaway, Kimberly P. Hodges, Reuven Ma, Yichen Moon, Alex Salois, Kyle |
| contents | Kohnert polynomials and their associated posets are combinatorial objects with deep geometric and representation theoretic connections, generalizing both Schubert polynomials and type A Demazure characters. In this paper, we explore the properties of Kohnert polynomials and their posets indexed by northeast diagrams. We give separate classifications of the bounded, ranked, and multiplicity-free Kohnert posets for northeast diagrams, each of which can be computed in polynomial time with respect to the number of cells in the diagram. As an initial application, we specialize these classifications to simple criteria in the case of lock diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kohnert posets and polynomials of northeast diagrams Bingham, Aram Castellano, Beth Anne Hadaway, Kimberly P. Hodges, Reuven Ma, Yichen Moon, Alex Salois, Kyle Combinatorics 05E99 Kohnert polynomials and their associated posets are combinatorial objects with deep geometric and representation theoretic connections, generalizing both Schubert polynomials and type A Demazure characters. In this paper, we explore the properties of Kohnert polynomials and their posets indexed by northeast diagrams. We give separate classifications of the bounded, ranked, and multiplicity-free Kohnert posets for northeast diagrams, each of which can be computed in polynomial time with respect to the number of cells in the diagram. As an initial application, we specialize these classifications to simple criteria in the case of lock diagrams. |
| title | Kohnert posets and polynomials of northeast diagrams |
| topic | Combinatorics 05E99 |
| url | https://arxiv.org/abs/2501.18030 |