860 research outputs found
Semisymmetric cubic graphs of twice odd order
The groups which can act semisymmetrically on a cubic graph of twice odd
order are determined modulo a normal subgroup which acts semiregularly on the
vertices of the graph
Musical Actions of Dihedral Groups
The sequence of pitches which form a musical melody can be transposed or
inverted. Since the 1970s, music theorists have modeled musical transposition
and inversion in terms of an action of the dihedral group of order 24. More
recently music theorists have found an intriguing second way that the dihedral
group of order 24 acts on the set of major and minor chords. We illustrate both
geometrically and algebraically how these two actions are {\it dual}. Both
actions and their duality have been used to analyze works of music as diverse
as Hindemith and the Beatles.Comment: 27 pages, 11 figures. To appear in the American Mathematical Monthly
- …