1) If E is generated by an n-ary operation of degree 0 with no symmetries, we get that F(E)(k(n - 1) + 1) consists, as a vector space, of "parenthesized products" of k(n - 1) + 1 variables indexed by {1, .

2) Consider that E is generated by an n-ary operation [mu] of degree 1.

and more generally an element of F(E)(k(n - 1) + 1) by a rooted planar n-ary tree with levels and (k(n - 1) + 1)) leaves.

The relations that we consider will be quadratic in the sense that we compose two n-ary multiplications.

To compute the dual operad of the operad associated to n-ary algebras we need some differential graded operad.

Thus, in the first case, completion is an operation that takes a given n-ary relation R and n relata [a.

An unbiased binary relation R is said to be strictly symmetric if its completion by the objects a and b is always the same regardless of the argument- places to which they are assigned; and, more generally, an unbiased n-ary relation is said to be strictly symmetric in its distinct argument-places [[Alpha].

Accordingly, we might take the canonical notion of exemplification to be one that holds between a neutral n-ary relation R and two n-tples of objects [a.

6) Exception should be made for the degenerate version of the positionalist view in which each biased n-ary relation is taken to correspond to a neutral relation whose argument-places are the numerical positions 1, 2,.

5 An

n-ary second-order relation is a mapping that maps n-tuples of first-order relations (each with a prescribed number of arguments) and individuals to truth values.

n-ary Limited is a privately held company, headquartered in Dumfries, Scotland, United Kingdom.

Locate the dominant entities in a functional area, either through the natural relationships as obtained from the system requirements document, local

n-ary relationships, integrity constraints, abstractions, or by just being the central focus of many simple relationships.