We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...

In an earlier paper we considered the problem of determining the packing and covering constants for families of trees whose generating function^ satisfied a relation y = x(y) for some power series itiy. In the present paper we consider the problem for some families of trees whose generating functions satisfy a more complicated relation.

Let N , k, t, and v be positive integers. Let C be an N × k array with entries from an alphabet Σ of size v; we typically take Σ = {0, . . . , v − 1}. When (ν1, . . . , νt) is a t-tuple with νi ∈ Σ for 1 ≤ i ≤ t, (c1, . . . , ct) is a tuple of t column indices (ci ∈ {1, . . . , k}), and ci 6= cj whenever νi 6= νj , the t-tuple {(ci, νi) : 1 ≤ i ≤ t} is a t-way interaction. The array covers the ...