Zigzag and foxtrot terraces for Z~n

A terrace for Zn (a Zn terrace) is an arrangement (a1, a2, . . . , an) of the n elements of Zn such that the sets of differences ai+1 − ai and ai − ai+1 (i = 1, 2, . . . , n−1) together contain each element of Zn\{0} exactly twice. Various general constructions are given for Zn terraces of two special types: zigzag terraces and foxtrot terraces. Some special cases already appear in the literatures of recreational and combinatorial mathematics, of statistics, and of the map color theorem, though the term “terrace” is not used in these sources. Now some powerful generalisations of previous results are presented, along with some new constructions.