摘要:

We show that a finite distributive lattice can be embedded into the r.e. degrees preserving least and greatest element if and only if the lattice contains a join‐irreducible noncappable element.

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.1

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A graph is called dominating if its vertices can be labelled with integers in such a way that for every function ƒ: ω → ω the graph contains a ray whose sequence of labels eventually exceeds ƒ. We obtain a characterization of these graphs by producing a small family of dominating graphs with the property that every dominating graph must contain some member of the family.

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.16

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.25

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

If α = {α1, α2, …, αs}, where α1⩾ α2… ⩾ αs>0, is a partition ofnthen λαdenotes the associated irreducible character ofSn, the symmetric group on {1, 2, …,n}, and, ifc∈CSn, the group algebra generated byCandSn, thendc(·) denotes the generalized matrix function associated withc. Ifc1,c2∈CSnthen we writec1≼c2in casedc1(A) ⩾dc2(A) for eachn×npositive semi‐definite Hermitian matrixA. Ifc∈CSnandc(e) ≠ 0, whereedenotes the identity inSn, thenĉorĉdenotes (c(e))−1c.The main result, an estimate for the norms of tensors of a certain anti‐symmetry type, implies that if α = {α1, α2, …, αs, 1t} is a partition ofnsuch thats>1 and αs= 2, and α′ denotes {α1, α2, …, αs-1, 1t} then λ̂α≼ (λα, ⊗ λ{2})↑̂ where ↑ denotes character induction fromSn−2×S2toSn. This in turn implies that if α = {α1, α2, …, αs, 1t} withs>1, αs= 2, and β denotes {α1+ 2, α2, …, αs-1, 1t} then λ̂α≼ λ̂βwhich, in conjunction with other known results, provides many new inequalities among immanants. In particular it implies that the permanent function dominates all normalized immanants whose associated partitions are of rank 2, a result which has proved elusive for some years.We also consider the non‐relationship problem for immanants – that is the problem of identifying pairs, (α,β) such that λ̂α≼ λ̂βand λ̂β≼ λ̂αare both false.

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.40

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.61

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.73

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.83

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.93

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.100

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.1.109

出版商:Oxford University Press    

年代:2016

数据来源: WILEY