In this paper, we examine the class of "deco" polyominoes and the succession rule describing their construction. These polyominoes are enumerated according to their directed height by factorial numbers. By changing some aspects of the "factorial" rule, we obtain some succession rules that describe various "deco" polyomino subclasses. By enumerating the subclasses according to their height and width, we find the following well-known numbers: Stirling numbers of the first and second kind, Narayana and odd index Fibonacci numbers. We wish to point out how the changes made on the original succession rule yield some new succession rules that produce transcendental, algebraic and rational generating functions.

We show that the FIX type theory introduced by Crole and Pitts [3] can be encoded in variants of Abadi and Cardelli's object calculi. More precisely, we show that the FIX type theory presented with judgements of both equality and operational reduction can be translated into object calculi, and the translation proved sound. The translations we give can be seen as using object calculi as a metalanguge within which FIX can be represented; an analogy can be drawn with Martin Löf's Theory of Arities and Expressions. As well as providing a description of certain interesting recursive objects in terms of rather simpler expressions found in the FIX type theory, the translations will be of interest to those involved with the automation of operational semantics.

The complexity of computing, via threshold circuits, the iterated product and powering of fixed-dimension $k\times k$ matrices with integer or rational entries is studied. We call these two problems $\sf IMP_k$ and $\sf MPOW_k$, respectively, for short. We prove that: (i) For $k\geq2$, $\sf IMP_k$ does not belong to ${\rm TC}^0$, unless ${\rm TC}^0={\rm NC}^1$.newline (ii) For stochastic matrices : $\sf IMP_2$ belongs to ${\rm TC}^0$ while, for $k\geq3$, $\sf IMP_k$ does not belong to ${\rm TC}^0$, unless ${\rm TC}^0={\rm NC}^1$. (iii) For any k, $\sf MPOW_k$ belongs to ${\rm TC}^0$.

We introduce two new classes of codes, namely adjacent codes and codes with finite interpreting delay. For each class, we establish an extension of the defect theorem.

We consider the multiparty communication model defined in [4] using the formalism from [8]. First, we correct an inaccuracy in the proof of the fundamental result of [6] providing a lower bound on the nondeterministic communication complexity of a function. Then we construct several very hard functions, i.e., functions such that those as well as their complements have the worst possible nondeterministic communication complexity. The problem to find a particular very hard function was proposed in [7], where it has been shown that almost all functions are very hard. We also prove that combining two very hard functions by the Boolean operation xor gives a very hard function.

For a non-negative integer k, we say that a language L is k-poly-slender if the number of words of length n in L is of order ${\cal O}(n^k)$. We give a precise characterization of the k-poly-slender context-free languages. The well-known characterization of the k-poly-slender regular languages is an immediate consequence of ours.