A remark on B4-Sequences

A Remark on Parity Sequences

If n = 2, then the set j£ is closely related to the Fibonacci sequence; specifically, t GT2 iff the 7 term of the Fibonacci sequence is odd. We ask, for each w, which numbers are uniquely expressible as the sum of two distinct elements of Tn. In general, for any given w, one can determine exactly which numbers are uniquely expressible. If w = 2, it is easy to see that there are five such number...

A remark concerning graphical sequences

In “A note on a theorem of Erdös & Gallai” ([6]) one identifies the nonredundant inequalities in a characterization of graphical sequences. We explain how this result may be obtained directly from a simple geometrical observation involving weak majorization. A sequence of positive integers d1, d2, . . . , dp is called graphical if it is the degree sequence of a graph, i.e., there is a graph who...

A Remark on (C,1) Means of Sequences

tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Let (s n) be a real sequence, let (σ n) denote the sequence of averages of its first n partial sums. Let lim sup n σ n = β and lim inf n σ n = α, where β = α. We prove that lim sup n s n = β and lim inf n s ...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Remark on a Reply

1.1 In their original PNAS article Macy and Sato (2002) make it clear that their main point concerns social mobility (see, for instance, the abstract and the last section). Their central claim is the non-monotonic effect of mobility: with moderate mobility, they maintain, trust can be established; with too much mobility, trust and trustworthiness are undermined — and therefore their "warning fl...