Notices of the American Mathematical Society
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Featured Articles and Invitations from the AMS
Sudoku Squares and Chromatic Polynomials
Agnes M. Herzberg and M. Ram Murty
The authors interpret the nine by nine Sudoku puzzle as a graph coloring problem. Viewed this way, they can generalize the puzzle to arbitrary size. They compute the chromatic number of the resulting graph, and they estimate the number of "Sudoku squares" of any given size.
Two Problems That Shaped a Century of Lattice Theory
George Grätzer
Lattices are ordered sets for which every pair of elements has an upper and a lower bound. That natural examples of lattices, like the power set of a set, have additional properties which may not be consequences of the lattice axioms was recognized early in the twentieth century. As the author shows, basic questions about the relations among these properties have inspired research in the subject down to the present day.