Cores with distinct parts and bigraded Fibonacci numbers

@article{Paramonov2017CoresWD,
  title={Cores with distinct parts and bigraded Fibonacci numbers},
  author={Kirill Paramonov},
  journal={Discrete Mathematics},
  year={2017},
  volume={341},
  pages={875-888}
}
The notion of $(a,b)$-cores is closely related to rational $(a,b)$ Dyck paths due to Anderson's bijection, and thus the number of $(a,a+1)$-cores is given by the Catalan number $C_a$. Recent research shows that $(a,a+1)$ cores with distinct parts are enumerated by another important sequence- Fibonacci numbers $F_a$. In this paper, we consider the abacus description of $(a,b)$-cores to introduce the natural grading and generalize this result to $(a,as+1)$-cores. We also use the bijection with… CONTINUE READING
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