A Further Note on Runs in Independent Sequences

On Runs in Independent Sequences

Given an i.i.d. sequence of n letters from a finite alphabet, we consider the length of the longest run of any letter. In the equiprobable case, results for this run turn out to be closely related to the well-known results for the longest run of a given letter. For coin-tossing, tail probabilities are compared for both kinds of runs via Poisson approximation.

Note on regular and coregular sequences

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

A further note on mongolism in twins.

A Further Note on Alternatives to Bpref

This paper compares the robustness of information retrieval (IR) metrics to incomplete relevance assessments, using four different sets of graded-relevance test collections with submitted runs – two from TREC and two from NTCIR. We investigate the effect of reducing the original relevance data on discriminative power (i.e., how often statistical significance can be detected given the probabilit...

A Further Note on Inductive Generalization

In this paper, we develop the algorithm, given in Plotkin (1970), for finding the least generalization of two clauses, into a theory of inductive generalization. The types of hypothesis which can be formed are very simple. They all have the form: (x)Pxm Qx. We have been guided by ideas from the philosophy of science, following Buchanan (1966). There is no search for infallible methods of genera...

A Note on Independent Sets in Trees

We give a simple graph-theoretical proofthat the largest number ofmaximal independent vertex sets in a tree with n vertices is given by 2k+ if n 2k, m(T) 2 if n 2k + 1, a result first proved by Wilf [SIAM J. Algebraic Discrete Methods, 7 (I 986), pp. 125-130]. We also characterize those trees achieving this maximum value. Finally we investigate some related problems. Key words, independent vert...