The density zero ideal and the splitting number

2020 ◽  
Vol 171 (7) ◽  
pp. 102807
Author(s):  
Dilip Raghavan
Keyword(s):  
Splitting Number ◽  
Density Zero

scholarly journals Connected Numbers and the Embedded Topology of Plane Curves

2018 ◽  
Vol 61 (3) ◽  
pp. 650-658 ◽  
Author(s):  
Taketo Shirane
Keyword(s):  
Plane Curve ◽  
Smooth Curve ◽  
Plane Curves ◽  
Irreducible Curve ◽  
Galois Cover ◽  
Splitting Number

AbstractThe splitting number of a plane irreducible curve for a Galois cover is effective in distinguishing the embedded topology of plane curves. In this paper, we define the connected number of a plane curve (possibly reducible) for a Galois cover, which is similar to the splitting number. By using the connected number, we distinguish the embedded topology of Artal arrangements of degree b ≥ 4, where an Artal arrangement of degree b is a plane curve consisting of one smooth curve of degree b and three of its total inflectional tangents.

s -Maximal Nonbases of Density Zero

1977 ◽  
Vol s2-15 (1) ◽  
pp. 29-34 ◽  
Author(s):  
Melvyn B. Nathanson
Keyword(s):  
Density Zero

Splitting Number is NP-Complete

1998 ◽  
pp. 285-297 ◽  
Author(s):  
L. Faria ◽  
C. M. H. de Figueiredo ◽  
C. F. X. Mendonça
Keyword(s):  
Splitting Number ◽  
Np Complete

scholarly journals On a Theorem of Niven

1979 ◽  
Vol 22 (1) ◽  
pp. 113-115
Author(s):  
R. Sita Rama Chandra Rao ◽  
G. Sri Rama Chandra Murty
Keyword(s):  
Density Zero

In [4], Niven proved that the set A of integers for all s ≥ l and all n ≥ 1 has density zero, being the sum of the sth powers of all positive divisors of n. However his argument contains a mistake (see Remark 1). In this paper we give a proof of Niven's result and establish several related results, one of which generalizes a result of Dressier (See Theorem 3 and Remark 2).

scholarly journals On the cofinality of the splitting number

2018 ◽  
Vol 29 (1) ◽  
pp. 382-395 ◽  
Author(s):  
Alan Dow ◽  
Saharon Shelah
Keyword(s):  
Splitting Number

The splitting number of complete bipartite graphs

1984 ◽  
Vol 42 (2) ◽  
pp. 178-184 ◽  
Author(s):  
B. Jackson ◽  
G. Ringel
Keyword(s):  
Bipartite Graphs ◽  
Splitting Number ◽  
Complete Bipartite Graphs

Nonbases of Density Zero not Contained in Maximal Nonbases

1977 ◽  
Vol s2-15 (3) ◽  
pp. 403-405 ◽  
Author(s):  
Paul Erdős ◽  
Melvyn B. Nathanson
Keyword(s):  
Density Zero

Splitting number at uncountable cardinals

1997 ◽  
Vol 62 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Jindřich Zapletal
Keyword(s):  
Large Cardinal ◽  
Inner Models ◽  
Splitting Number ◽  
Uncountable Cardinal ◽  
Uncountable Cardinals

AbstractWe study a generalization of the splitting number s to uncountable cardinals. We prove that 𝔰(κ) > κ+ for a regular uncountable cardinal κ implies the existence of inner models with measurables of high Mitchell order. We prove that the assumption 𝔰(ℵω) > ℵω+1 has a considerable large cardinal strength as well.

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