An extension of the Lindström-Gessel-Viennot theorem
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866915959666638848 |
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| author | Lee, Yi-Lin |
| author_facet | Lee, Yi-Lin |
| contents | Consider a weighted directed acyclic graph $G$ having an upward planar drawing. We give a formula for the total weight of the families of non-intersecting paths on $G$ with any given starting and ending points. While the Lindström-Gessel-Viennot theorem gives the signed enumeration of these weights (according to the connection type), our result provides the straight count, expressing it as a determinant whose entries are signed counts of lattice paths with given starting and ending points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_06115 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An extension of the Lindström-Gessel-Viennot theorem Lee, Yi-Lin Combinatorics 05A15, 05C30, 05C38 Consider a weighted directed acyclic graph $G$ having an upward planar drawing. We give a formula for the total weight of the families of non-intersecting paths on $G$ with any given starting and ending points. While the Lindström-Gessel-Viennot theorem gives the signed enumeration of these weights (according to the connection type), our result provides the straight count, expressing it as a determinant whose entries are signed counts of lattice paths with given starting and ending points. |
| title | An extension of the Lindström-Gessel-Viennot theorem |
| topic | Combinatorics 05A15, 05C30, 05C38 |
| url | https://arxiv.org/abs/2112.06115 |