#R_D

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2025-06-30

アニメづくりのR&D座談会 2025 No.2/R&Dの火を絶やさぬための組織戦略 - 特集
cgworld.jp/article/202506-rad-

#cgworld #アニメ #アーチ #オー_エル_エム_デジタル #グラフィニカ #東映アニメーション #R_D

アニメづくりのR&D座談会 2025 No.1/アニメ業界の未来を拓く、攻めと守りのR&D戦略 - 特集
cgworld.jp/article/202506-rad-

#cgworld #アニメ #アーチ #オー_エル_エム_デジタル #グラフィニカ #東映アニメーション #R_D

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2025-06-11
2025-03-28

Matchgate signatures under variable permutations

Boning Meng, Yicheng Pan
arxiv.org/abs/2503.21194 arxiv.org/pdf/2503.21194 arxiv.org/html/2503.21194

arXiv:2503.21194v1 Announce Type: new
Abstract: 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.

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