Counting filter restricted paths in $\mathbb{Z}^2$ lattice
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914760579088384 |
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| author | Postnova, Olga Solovyev, Dmitry |
| author_facet | Postnova, Olga Solovyev, Dmitry |
| contents | We derive a path counting formula for two-dimensional lattice path model on a plane with filter restrictions. A filter is a line that restricts the path passing it to one of possible directions. Moreover, each path that touches this line is assigned a special weight. The periodic filter restrictions are motivated by the problem of tensor power decomposition for representations of quantum $\mathfrak{sl}_2$ at roots of unity. Our main result is the explicit formula for the weighted number of paths from the origin to a fixed point between two filters in this model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2107_09774 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Counting filter restricted paths in $\mathbb{Z}^2$ lattice Postnova, Olga Solovyev, Dmitry Combinatorics We derive a path counting formula for two-dimensional lattice path model on a plane with filter restrictions. A filter is a line that restricts the path passing it to one of possible directions. Moreover, each path that touches this line is assigned a special weight. The periodic filter restrictions are motivated by the problem of tensor power decomposition for representations of quantum $\mathfrak{sl}_2$ at roots of unity. Our main result is the explicit formula for the weighted number of paths from the origin to a fixed point between two filters in this model. |
| title | Counting filter restricted paths in $\mathbb{Z}^2$ lattice |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2107.09774 |