All quadrirational Yang-Baxter maps in a key subclass on positive reals have the independence preserving property and generate most known IP bijections via specialization or limits.
V eselov,Yang–baxter maps and integrable dynamics, Physics Letters A 314 (2003), no
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Yang-Baxter maps and independence preserving property
All quadrirational Yang-Baxter maps in a key subclass on positive reals have the independence preserving property and generate most known IP bijections via specialization or limits.