The existence of (p,q)-extended Rosa sequences Original Research Article

A (image)-extended Rosa sequence is a sequence of length image containing each of the symbols image exactly twice, and such that two occurrences of the integer image are separated by exactly image symbols. We prove that, with two exceptions, the conditions necessary for the existence of a (image)-extended Rosa sequence with prescribed positions of the symbols 0 are sufficient. We also extend the result to image-fold (image)-extended Rosa sequences; i.e., the sequences where every pair of numbers is repeated exactly image times.