Name
Abstract | ||
|---|---|---|
Given a G-space X and a non-trivial G-invariant ideal I of subsets of X, we prove that for every partition X = A(1) boolean OR . . . boolean OR A(n) of X into n >= 2 pieces there is a piece A(i) of the partition and a finite set F subset of G of cardinality vertical bar F vertical bar <= phi(n + 1) := max(1<x<n+1) x(n+1-x -1)/x-1 such that G = F.Delta(A(i)) where Delta(A(i)) = {g is an element of G: gA(i) boolean AND A(i) is not an element of I} is the difference set of the set A(i). Also we investigate the growth of the sequence phi(n) = max(1< x<n) x(n-x-1)/x-1 and show that ln phi(n+1) = nW(ne)-2n + n/(W(ne)) + W(ne)/n + O(ln ln n/n) where W(x) = ln x-ln ln x + O(ln ln x/ln x) is the Lambert W-function, defined implicitly as W(x)e(W(x)) = x. This shows that phi(n) grows faster than that any exponent a(n) but slower than the sequence n! of factorials. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1142/S0218196716500132 | INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION |
Keywords | Field | DocType |
G-space, G-lattice, partition, large set | Discrete mathematics,Combinatorics,Finite set,Algebra,Lattice (order),Exponent,Difference set,Cardinality,Partition (number theory),Mathematics | Journal |
Volume | Issue | ISSN |
26 | 2 | 0218-1967 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Taras O. Banakh | 1 | 9 | 7.24 |
| Oleksandr Ravsky | 2 | 0 | 0.34 |
| Sergiy Slobodianiuk | 3 | 0 | 1.01 |