Partition identities and quiver representations
| Autor: | Richárd Rimányi, Alexander Yong, Anna Weigandt |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Quiver Cauchy distribution 0102 computer and information sciences 01 natural sciences Bijective proof Combinatorics 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Partition (number theory) Combinatorics (math.CO) 0101 mathematics Mathematics::Representation Theory Durfee square Mathematics |
| Zdroj: | Journal of Algebraic Combinatorics. 47:129-169 |
| ISSN: | 1572-9192 0925-9899 |
| DOI: | 10.1007/s10801-017-0771-5 |
| Popis: | We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy's Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke's identity in the case of quivers $Q$ of Dynkin type $A$ of arbitrary orientation. Our identity is stated in terms of the lacing diagrams of S. Abeasis - A. Del Fra, which parameterize orbits of the representation space of $Q$ for a fixed dimension vector. 26 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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