MathDBThe d-complete-poset LE-cactus conjecture
The d-complete-poset LE-cactus conjecture
Let be a d-complete poset. A poset is LE-cactus when its Bender–Knuth group action on its linear extensions satisfies the cactus relations. The d-complete-poset LE-cactus conjecture. Every d-complete poset is LE-cactus. This extends the verified result for minuscule posets and other motivating families; the general case remains open.
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Sources & referencesView supporting material
Primary source
Judy Hsin-Hui Chiang, Anh Trong Nam Hoang, Matthew Kendall, Ryan Lynch, Son Nguyen, Benjamin Przybocki and Janabel Xia, “Bender-Knuth involutions on linear extensions of posets”, arXiv:2302.12425 (2024).
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