摘要:

SupposeAis annk×nkpositive semi-definite symmetric matrix partitioned into blocksAijeach of which is ann×nmatrix. Letà = [aij] whereaij= per (Aij) for 1⩽i,j⩽kand let à = [bij] wherebij= |aij| for 1 ⩽i,j⩽k. A conjecture of Marcus is that per (A) ⩾ per (Â). In this paper we are able to show that for eachkthe stronger inequality per(A) ⩾ per (Ã) holds for all but finitely many integersnn.

ISSN:0308-1087    

DOI:10.1080/03081088208817427

出版商:Gordon and Breach Science Publishers    

年代:1982

数据来源: Taylor

摘要:

LetS(A) be the similarity class of ann×ndiagonal matrixAwith distinct eigenvalues and nonzero trace. The form of a linear transformation on then×nmatrices that preservesS{A) is determined.

ISSN:0308-1087    

DOI:10.1080/03081088208817428

出版商:Gordon and Breach Science Publishers    

年代:1982

数据来源: Taylor

摘要:

We consider scalar-valued matrix functions forn×nmatricesA=(aij) defined byWhereGis a subgroup ofSnthe group of permutations onnletters, and χ is a linear character ofG. Two such functions are the permanent and the determinant. A function (1) is multiplicative on a semigroupSofn×nmatrices ifd(AB)=d(A)d(B)AB∈S.

ISSN:0308-1087    

DOI:10.1080/03081088208817429

出版商:Gordon and Breach Science Publishers    

年代:1982

数据来源: Taylor

摘要:

LetRbe a commutative ring with 1R≠0 and letdenote the polynomial ring overRin indeterminatesXij=:(i∥j),i∈m={1,2,…m} andj∈n. To every bitableau (ST)S=(sij)(resp.T=(tij)) having all its entries inm(resp.n), one can associate the following polynomial in, which is the product of certain subpermanents "of the genericm×nmatrixX=(Xij) over. These so-called bipermanents, closely related to the principal characters of the symmetric groups, are analogues of the bideterminants, which correspond to the alternating characters of the symmetric groups. Doubilet, Rota and Stein proved that the. standard bideterminants form anR-basis of the polynomial ring(no further assumptions onRare necessary!). Such a global result does not hold for bipermanents. By homogeneity conditions one can decompose the polynomial ring into intertwining spacesRαβ(see [1, p. 162]). Besides a straightening formula for bipermanents I give—as a function on α and β—a necessary and sufficient condition onRunder which the standard bipermanents of content (αβ) form anR-basis ofRαβ

ISSN:0308-1087    

DOI:10.1080/03081088208817430

出版商:Gordon and Breach Science Publishers    

年代:1982

数据来源: Taylor

摘要:

A simple derivation is given of a well-known relation involving the so-called "Cayley Operator" of classical invariant theory. The proof is induction-free and independent of Capelli's identity; it makes use only of a known-theorem in the theory of determinants and some elementary combinatorics.

ISSN:0308-1087    

DOI:10.1080/03081088208817431

出版商:Gordon and Breach Science Publishers    

年代:1982

数据来源: Taylor

摘要:

We give a bijective proof of a formula due independently to Frobenius and Young for the number of standard Young tableau of shape λ for λ any partition. Frame, Robinson, and Thrall derived their hook formula for the number of standard Young tableau from the Frobenius-Young formula. As a corollary to our bijective proof of the Frobenius-Young formula, we also give a bijective proof of the Frame-Robinson-Thrall hook formula.

ISSN:0308-1087    

DOI:10.1080/03081088208817432

出版商:Gordon and Breach Science Publishers    

年代:1982

数据来源: Taylor

ISSN:0308-1087    

DOI:10.1080/03081088208817433

出版商:Gordon and Breach Science Publishers    

年代:1982

数据来源: Taylor

摘要:

Applied Combinatorics, by Alan Tucker. Wiley, 1980, 385 pages

ISSN:0308-1087    

DOI:10.1080/03081088208817434

出版商:Gordon and Breach Science Publishers    

年代:1982

数据来源: Taylor