  A multi-crossing (or n-crossing) is a singular point in a projection at which
n strands cross so that each strand bisects the crossing. We generalize the
classic result of Kauffman, Murasugi, and Thistlethwaite, which gives the upper
bound on the span of the bracket polynomial of K as 4c_2(K), to the n-crossing
number: span<K> is bounded above by ([n^2/2] + 4n-8) c_n(K) for all integers n
at least 3.
  We also explore n-crossing additivity under composition, and find that for n
at least 4, there are examples of knots such that the n-crossing number is
sub-additive. Further, we present the first extensive list of calculations of
n-crossing numbers for knots. Finally, we explore the monotonicity of the
sequence of n-crossings of a knot, which we call the crossing spectrum.
