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- W77881810 abstract "Let $lambda$ be a partition, viewed as a Young diagram. We define the hook difference of a cell of $lambda$ to be the difference of its leg and arm lengths. Define $h_{1,1}(lambda)$ to be the number of cells of $lambda$ with hook difference one. In the paper of Buryak and Feigin (arXiv:1206.5640), algebraic geometry is used to prove a generating function identity which implies that $h_{1,1}$ is equidistributed with $a_2$, the largest part of a partition that appears at least twice, over the partitions of a given size. In this paper, we propose a refinement of the theorem of Buryak and Feigin and prove some partial results using combinatorial methods. We also obtain a new formula for the q-Catalan numbers which naturally leads us to define a new q,t-Catalan number with a simple combinatorial interpretation." @default.
- W77881810 created "2016-06-24" @default.
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- W77881810 date "2014-04-30" @default.
- W77881810 modified "2023-09-23" @default.
- W77881810 title "Partition Statistics Equidistributed with the Number of Hook Difference One Cells" @default.
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- W77881810 doi "https://doi.org/10.48550/arxiv.1405.0072" @default.
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