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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.00175 |
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| _version_ | 1866912159327322112 |
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| author | Fischer, Ilse |
| author_facet | Fischer, Ilse |
| contents | An identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that alternating sign trapezoids are equinumerous with holey cyclically symmetric lozenge tilings of a hexagon. We establish a bounded version of a generalization of this identity. Further, we provide combinatorial interpretations of both sides of the identity. The ultimate goal would be to construct a combinatorial proof of this identity (possibly via an appropriate variant of the Robinson-Schensted-Knuth correspondence) and its unbounded version as this would improve the understanding of the relation between alternating sign trapezoids and plane partition objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00175 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bounded Littlewood identity related to alternating sign matrices Fischer, Ilse Combinatorics Mathematical Physics An identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that alternating sign trapezoids are equinumerous with holey cyclically symmetric lozenge tilings of a hexagon. We establish a bounded version of a generalization of this identity. Further, we provide combinatorial interpretations of both sides of the identity. The ultimate goal would be to construct a combinatorial proof of this identity (possibly via an appropriate variant of the Robinson-Schensted-Knuth correspondence) and its unbounded version as this would improve the understanding of the relation between alternating sign trapezoids and plane partition objects. |
| title | Bounded Littlewood identity related to alternating sign matrices |
| topic | Combinatorics Mathematical Physics |
| url | https://arxiv.org/abs/2301.00175 |