Overlap of words complicates the problem of word counting. The technique of the imbedded Markov chain (IMC) uses an enlarged state space to recover the Markovian property for the word counting problem. A degenerate word represents multiple non-degenerate words. An efficient way to decompose a degenerate word according to its overlapping pattern for implementing IMC is proposed.

A degenerate or indeterminate string on an alphabet Σ is a sequence of non-empty subsets of Σ. Given a degenerate string t of length n, we present a new method based on the Burrows–Wheeler transform for searching for a degenerate pattern of length m in t running in O(mn) time on a constant size alphabet Σ. Furthermore, it is a hybrid patternmatching technique that works on both regular and dege...

We study the functional codes of second order defined by G. Lachaud on X ⊂ P(Fq) a quadric of rank(X )=3,4,5 or a non-degenerate hermitian variety. We give some bounds for the number of points of quadratic sections of X , which are the best possible and show that codes defined on non-degenerate quadrics are better than those defined on degenerate quadrics. We also show the geometric structure o...

This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a nondegenerate chainable continuum. This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a non-degenerate chainable continuum. By R.H. Bing’s theorem eleven [2] if a metric continuum X contains a non-degenerate subconti...

We show that in the worst case, Q(nd) sidedness queries are required to determine whether a set of n points in Rd is affinely degenerate, i .e . , whether it contains d + 1 points on a common hyperplane. This matches known upper bounds. We give a straightforward adversary argument, based on the explicit construction of a point set containing Q(nd) “collapsible” simplices, any one of which can b...

Degenerate Dowling and degenerate r-Dowling polynomials were introduced earlier as versions further generalizations of polynomials. The aim this paper is to show their connections with Poisson central moments for a random variable certain parameter Charlier