Matchgate signatures under variable permutations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917968978378752 |
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| author | Meng, Boning Pan, Yicheng |
| author_facet | Meng, Boning Pan, Yicheng |
| contents | In this article, we give a sufficient and necessary condition for determining whether a matchgate signature retains its property under a certain variable permutation, which can be checked in polynomial time. We also define the concept of permutable matchgate signatures, and use it to erase the gap between Pl-\#CSP and \#CSP on planar graphs in the previous study. We provide a detailed characterization of permutable matchgate signatures as well, by presenting their relation to symmetric matchgate signatures. In addition, we prove a dichotomy for Pl-$\#R_D$-CSP where $D\ge 3$ is an integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matchgate signatures under variable permutations Meng, Boning Pan, Yicheng Combinatorics Computational Complexity In this article, we give a sufficient and necessary condition for determining whether a matchgate signature retains its property under a certain variable permutation, which can be checked in polynomial time. We also define the concept of permutable matchgate signatures, and use it to erase the gap between Pl-\#CSP and \#CSP on planar graphs in the previous study. We provide a detailed characterization of permutable matchgate signatures as well, by presenting their relation to symmetric matchgate signatures. In addition, we prove a dichotomy for Pl-$\#R_D$-CSP where $D\ge 3$ is an integer. |
| title | Matchgate signatures under variable permutations |
| topic | Combinatorics Computational Complexity |
| url | https://arxiv.org/abs/2503.21194 |