For our proof we develop techniques for flip sequences of triangulations whose counterparts were introduced for the study of flip sequences of non-crossing spanning trees by Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber~[SODA25] and Bjerkevik, Dorfer, Kleist, Ueckerdt, and Vogtenhuber~[SoCG26].
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When updating the rows we’ll only need to update the Y coordinates, but we do need a table of subsequent Y coordinates. That’s one row shorter than usual because we handled the top row as part of the original shadow_loc definition:，这一点在体育直播中也有详细论述
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