Bender-Knuth Involutions on Linear Extensions of Posets.

We study the permutation group BK P generated by Bender–Knuth moves on linear extensions of a poset P, an analog of the Berenstein–Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on identifying posets P for which the cactus relations hold in BK P. We also examine BK P as a subgroup of the symmetric group S L ( P ) on the set of linear extensions of P with the focus on analyzing posets P for which BK P = S L ( P ).