B.S.T.J. Briefs: All Terminal Bubbles Programs Yield the ElementarySymmetric Polynomials

All Terminal Bubbles Programs Yield the Elementary Symmetric Polynomials By R. P. KURSHAN (Manuscript received May 18, 1970) R. L. Graham has discussed various combinatorial aspects of the behavior of magnetic domains or "bubbles". 1 Representing the initial state of a configuration of n magnetic domains by the n-tuple of indeterminates B = (XXl · · · , Xn), he showed that subsequent configurations of magnetic domains obtainable (within the constraints of the problem) correspond exactly to subsequent n-tuples of Boolean expressions in the X.'s* obtainable from B through an application to B of a product of transformations ("commands" in Ref. 1) of the form Tu( 1 Ik i