Asymptotic Analysis of Regular Sequences

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.

Remarks on Regular Sequences

In this note we exhibit a condition under which a sequence of elements a19 , an in a commutative noetherian local ring A form an Asequence, and derive a number of corollaries. Recall that if M is an A-module, then a19 , an is an M-sequence if 1) ai+1 is a nonzerodivisor on M/(a19 9a1)M for i = 0, 9n — 1,. and 2) M Φ (al9 . . . , α n ) M . If a19 , an is an A-sequence and / is the ideal generate...

Asymptotic Behavior of Moment Sequences

In this paper we study asymptotic behavior of some moment spaces. We consider two different settings. In the first one, we work with ordinary multi-dimensional moments on the standard m-simplex. In the second one, we deal with the trigonometric moments on the unit circle of the complex plane. We state large and moderate deviation principles for uniformly distributed moments. In both cases the r...

The Asymptotic Density of Sequences

The Asymptotic Number of Unlabelled Regular Graphs

Over ten years ago Wright [4] proved a fundamental theorem in the theory of random graphs. He showed that if M = M(n) is such that almost no labelled graph of order n and size M has two isolated vertices or two vertices of degree n — 1, then the number of labelled graphs of order n and size M divided by the number of unlabelled graphs of order n and size M is asymptotic to n\. The result is bes...