The discriminator of an integer sequence s = (s(i))i≥0, introduced by Arnold, Benkoski, and McCabe in 1985, is the map Ds(n) that sends n ≥ 1 to the least positive integer m such that the n numbers s(0), s(1), . . . , s(n − 1) are pairwise incongruent modulo m. In this note we consider the discriminators of a certain class of sequences, the k-regular sequences. We compute the discriminators of ...

In the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. Let be a double sequence of pairwise negatively dependent random variables. If for all non-negative real numbers t and , for 1 < p < 2, then we prove that (1). In addition, it also converges to 0 in ....

A typical approach to handle the complexity of multi-faceted decision-making problems is to use multiattribute decision-making (MADM) methods based on pairwise comparisons. Fuzzy set theory has also been employed to cope with the uncertainty and vagueness involved in conducting the comparisons between components of a decision model. An important issue regarding the reliability of the output is ...

It is shown that every cyclic split system S defined on an n-set with #S > 2kn− (2k+1 2 ) for some k ≤ n−1 2 always contains a subset of k+1 pairwise incompatible splits provided one has min(k, n−(2k+1)) ≤ 3. In addition, some related old and new conjectures are also discussed.

We study partitions of the set of all cyclic (respectively, transitive) triples chosen from a v-set into pairwise disjoint MTS(4)s (respectively, DTS(4)s). We find necessary conditions for the partitions. Furthermore, we prove that the necessary conditions for the partitions are also sufficient.

We show that a graph-like continuum embeds in some surface if and only if it does not contain one of: a generalized thumbtack; or infinitely many K3,3’s or K5’s that are either pairwise disjoint or all have just a single point in common.