Subconstituent

In any metrical tree or constituent, the HTE of the subconstituent dominated by l is: a. One register step lower than the HTE of the subconstituent dominated by h when the l subconstituent is on the right; b. at the same register as the HTE of the subconstituent dominated by h when the l subconstituent is on the left.

The dominance relation directly characterizes the property of subconstituency: X dominates Y if Y is a subconstituent of X.

Given two adjacent constituents A and B, two cases must be considered: * A can attach as a left subconstituent of B; * B can attach as a right subconstituent of A, or as a right subconstituent of an active subconstituent of A.

The second subconstituent of a graph with respect to some vertex x is the induced graph on the vertices distinct from x, and that are not adjacent to x.

During 1992 and 1993 Paul Terwilliger introduced a new tool called the subconstituent algebra for studying the underlying structure of association schemes through a series of three papers [21], [22], and [23]. Terwilliger introduced a method for studying commutative association schemes by defining a new algebra that is noncommutative, finite dimensional, semisimple C-algebra. The subconstituent algebra is now popularly referred to as the "Terwilliger" algebra.

The term prequark has appeared in the literature as a name for subconstituents in composite models [4].

Apart from hadrons, which are made of subconstituent quarks, electron and positron are “fundamental” objects.

Subconstituent models of quarks, leptons and the weak gauge bosons [4] sometimes employ the idea of "Chiral Confinement [5] .