A large number of diversity measures have been proposed in the literature, almost all which are designed for sets with elements that differ multiple aspects. However, these types not appropriate a single aspect only, such as duration, value or probability. In this essay I present new measure diversity, specifically diversity. The captures intuitive idea is affected by maximal dissimilarity betw...

1 Definitions and basic examples of Boolean algebras Definition 1.1. A partially ordered set (or poset for short) is a pair X, ≤ X where X is a nonempty set, ≤ X is a binary relation on X with the following properties for all x, y, z ∈ X: If, in addition, X, ≤ X satisfies the property (x ≤ X y ∨ y ≤ X x) for all x and y, then it is called a total or linear order. We frequently drop the subscrip...

The maximal sum of a sequence A of n real numbers is the greatest sum of all elements of any linearly contiguous and possibly empty subsequence of A. It can be computed in O(n) time by means of Kadane’s algorithm. Letting A denote the sequence which results from inserting a real number x between elements A[p− 1] and A[p], we show how the maximal sum of A can be computed in O(1) worst-case time ...

In many combinatorial situations there is a notion of independence of a set of points. Maximal independent sets can be easily constructed by a greedy algorithm, and it is of interest to determine, for example, if they all have the same size or the same parity. Both of these questions may be formulated by weighting the points with elements of an abelian group, and asking whether all maximal inde...

We describe a new class of maximal cliques, with vector space structure, Cayley graphs defined on the additive group field. In particular, we show that in cubic Paley graph order $q^3$, subfield $q$ elements forms clique. Similar statements also hold for quadruple and Peisert quartic order.

A complete arc in a design is a set of elements which contains no block, and is maximal with respect to this property. The spectrum of sizes of complete arcs in Steiner triple systems is determined without exception here.

In this paper we define a new concept of monitoring the elements of triangulation graphs by faces. Furthermore, we analyze this, and other monitoring concepts (by vertices and by edges), from a combinatorial point of view, on maximal outerplanar graphs.

We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms of the number of its minimal monomial generators and the maximal height of its minimal primes.

Let M be a triangulable compact manifold. We prove that, among closed subgroups of Homeo0(M) (the identity component of the group of homeomorphisms of M), the subgroup consisting of volume preserving elements is maximal. AMS classification. 57S05 (57M60, 37E30).

A subset X of vertices and edges of a graph G is totally matching if no two elements of X are adjacent or incident. In this paper we determine all graphs in which every maximal total matching is maximum.