Percolating sets and the operad of permutations

Abstract: We give an operadic interpretation of the known result of L.Shapiro and A.B.Stephens that characterizes percolating permutation matrices. A relation of ideals and suboperads of the non-symmetric operad of permutations to percolative properties of sets in the 2-neighbor percolation process is discussed. On a related note, we discuss a certain presentation of the operad of permutations.