Riasat, Samin2019-08-282019-08-282019-08-282019-08-15http://hdl.handle.net/10012/14974Fici et al. recently introduced the notion of anti-powers in the context of combinatorics on words. A power (also called tandem repeat) is a sequence of consecutive identical blocks. An anti-power is a sequence of consecutive distinct blocks of the same length. Fici et al. showed that the existence of powers or anti-powers is an unavoidable regularity for sufficiently long words. In this thesis we explore this notion further in the context of binary words and obtain new results.encobinatorics on wordsramsey theoryanti powerMaster Thesis