Non-intersecting paths and the determinant of the distance matrix of a tree
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910975332974592 |
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| author | Briand, Emmanuel Esquivias-Quintero, Luis Gutiérrez, Álvaro Lillo, Adrián Rosas, Mercedes |
| author_facet | Briand, Emmanuel Esquivias-Quintero, Luis Gutiérrez, Álvaro Lillo, Adrián Rosas, Mercedes |
| contents | We present the first combinatorial proof of the Graham-Pollak Formula for the determinant of the distance matrix of a tree, via sign-reversing involutions and the Lindström-Gessel-Viennot Lemma. Our approach provides a cohesive and unified framework for the understanding of the existing generalizations and $q$-analogues of the Graham-Pollak Formula, and facilitates the derivation of a natural simultaneous generalizations for them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-intersecting paths and the determinant of the distance matrix of a tree Briand, Emmanuel Esquivias-Quintero, Luis Gutiérrez, Álvaro Lillo, Adrián Rosas, Mercedes Combinatorics 05C05 (Primary) 05A19, 05A15 (Secondary) We present the first combinatorial proof of the Graham-Pollak Formula for the determinant of the distance matrix of a tree, via sign-reversing involutions and the Lindström-Gessel-Viennot Lemma. Our approach provides a cohesive and unified framework for the understanding of the existing generalizations and $q$-analogues of the Graham-Pollak Formula, and facilitates the derivation of a natural simultaneous generalizations for them. |
| title | Non-intersecting paths and the determinant of the distance matrix of a tree |
| topic | Combinatorics 05C05 (Primary) 05A19, 05A15 (Secondary) |
| url | https://arxiv.org/abs/2407.01227 |