category_of_non-crossing_partitions_with_blocks_of_even_size
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category_of_non-crossing_partitions_with_blocks_of_even_size [2020/01/22 08:59] amang created |
category_of_non-crossing_partitions_with_blocks_of_even_size [2021/11/23 11:56] (current) |
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| * The name **set of all non-crossing partitions with blocks of even size** is to be taken literally. | * The name **set of all non-crossing partitions with blocks of even size** is to be taken literally. | ||
| - | A partition with blocks of even size is in particular of even size itself. Moreover, such a partition, if additionally non-crossing, necessarily also has even distances between legs. | + | A partition with blocks of even size is in particular of even size itself. Moreover, such a partition, if additionally non-crossing, necessarily also has parity-balanced legs. |
| ===== Canonical generator ===== | ===== Canonical generator ===== | ||
| - | The category of non-crossing partitions with blocks of even size is the subcategory of $\Pscr$ generated by the partition $\fourpart$. | + | The category of non-crossing partitions with blocks of even size is the subcategory of $\Pscr$ generated by the partition $\fourpart$. |
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| + | ===== Counting ===== | ||
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| + | $$\#\Cscr(0,2k)={1\over 2k+1}{3k\choose k}$$ | ||
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| + | See [[https://oeis.org/A001764|OEIS A001764]] | ||
| ===== Associated easy quantum groups ===== | ===== Associated easy quantum groups ===== | ||
category_of_non-crossing_partitions_with_blocks_of_even_size.1579683588.txt.gz · Last modified: 2021/11/23 11:56 (external edit)
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