Algebra & Combinatorics Research Group  |  Texas A&M University





A&C Seminar

Working Seminar
   in Algebra

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A&C Seminar:  Fall 2008, Fridays, Milner 317, 3:00–3:50 p.m.

September 5 Aaron Lauve (TAMU)
3:00–3:50 The Markoff condition and central words
Abstract:   During his study of binary quadratic forms aX2 + bXY + cY2 in the late 1800s, Markoff introduced necessary and sufficient conditions on a reduced form f so that its minimum is less than 3. He phrased his condition in terms certain forbidden patterns of a bi-infinite word associated to f. From the Markoff condition one gets a large class of binary words that we call Markoff words. In this talk, we will see that the Markoff words are palindromes, and indeed are the important central words from the theory of Sturmian sequences. (This is joint work with Amy Glen and Franco Saliola.)