Saturation property fails for Schubert coefficients
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912808200830976 |
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| author | Pak, Igor Robichaux, Colleen |
| author_facet | Pak, Igor Robichaux, Colleen |
| contents | The saturation property for Littlewood--Richardson coefficients was established by Knutson and Tao in 1999. In 2004, Kirillov conjectured that the saturation property extends to Schubert coefficients. We disprove this conjecture in a strong form, by showing that it fails for a large family of instances. We also refute the saturation property for Schubert coefficients under bit scaling and discuss computational complexity implications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04182 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Saturation property fails for Schubert coefficients Pak, Igor Robichaux, Colleen Combinatorics Primary: 05E14, Secondary: 05E10, 14M15, 14N15 The saturation property for Littlewood--Richardson coefficients was established by Knutson and Tao in 1999. In 2004, Kirillov conjectured that the saturation property extends to Schubert coefficients. We disprove this conjecture in a strong form, by showing that it fails for a large family of instances. We also refute the saturation property for Schubert coefficients under bit scaling and discuss computational complexity implications. |
| title | Saturation property fails for Schubert coefficients |
| topic | Combinatorics Primary: 05E14, Secondary: 05E10, 14M15, 14N15 |
| url | https://arxiv.org/abs/2601.04182 |