We use combinatorial and generating function techniques to enumerate various sets of involutions which avoid 231 or contain 231 exactly once. Interestingly, many of these enumerations can be given in terms of k-generalized Fibonacci numbers.

We propose the first algebraic determinantal formula to enumerate tilings of a centro-symmetric octagon of any size by rhombi. This result uses the Gessel-Viennot technique and generalizes to any octagon a formula given by Elnitsky in a special case.

The cross-section enumeration problem is to list all words of length n in a regular language L in lexicographical order. The enumeration problem is to list the rst m words in L according to radix order. We present an algorithm for the crosssection enumeration problem that is linear in n + t, where t is the output size. We provide a detailed analysis of the asymptotic running time of our algorit...

The cross-section enumeration problem is to list all words of length n in a regular language L in lexicographical order. The enumeration problem is to list the first m words in L according to radix order. We present an algorithm for the cross-section enumeration problem that is linear in n. We provide a detailed analysis of the asymptotic running time of our algorithm and that of known algorith...

We discuss a notion of forcing that characterises enumeration 1genericity and we investigate the immunity, lowness and quasiminimality properties of enumeration 1-generic sets and their degrees. We construct an enumeration operator ∆ such that, for any A, the set ∆ is enumeration 1-generic and has the same jump complexity as A. We also prove that every nonzero ∆ 2 degree bounds a nonzero enumer...

Fault diagnosis is to predict the potential fault sites in a logic IC. In this paper, we particularly address the problem of diagnosing faults that exhibit the so-called Byzantine General’s phenomenon, in which a fault manifests itself as a non-logical voltage level at the fault site. Previously, explicit enumeration was suggested to deal with such a problem. However, it is often too time-consu...

In this paper we describe applications of functions from GF(2) m onto GF(2) n in the design of encryption algorithms. If such a function is to be useful it must satisfy a set of criteria, the actual definition of which depends on the type of encryption technique involved. This in turn means that it is important to ensure that the selected criteria do not restrict the choice of function too seve...

By the motivation to discover patterns in massive structured data in the form of graphs and trees, we study a special case of the ksubtree enumeration problem, originally introduced by (Ferreira, Grossi, and Rizzi, ESA’11, 275-286, 2011), where an input graph is a tree of n nodes. Based on reverse search technique, we present the first constant delay enumeration algorithm that lists all k-subtr...