How the odd terms in the Fibonacci sequence stack up

17 November 2005, 2:30 pm

 

Speaker: Prof D Rogers (Hawaii)

A polyomino is the natural generalization to finitely many cells of the square grid of the familiar domino. Although the word ``polyomino'' seems to have been coined by Solomon Golomb for a talk at the Harvard Mathematics Club in 1953, problems on this type of cellular structure seem to go back at least as far as Henry Dudeney, in 1907. But, of course, the Ferrars' diagrams of the theory of partitions might also be viewed as special types of polyominoes. Moreover, placing two Ferrars' diagrams back-to-back gives the sort of stack polyomino considered by H.N.V. Templerley in the late 1940s as a model of crystal growth. This provides the background for a discussion of various enumeration problems of classes of polyominoes that can be characterized by path connectedness.