摘要:

Results are obtained on the likely connectivity properties and sizes of circuits in the column dependence matroid of a randomr×nmatrix over a finite field, for largerandn. In a sense made precise in the paper, it is shown to be highly probable that whennis less thanrsuch a matroid is the free matroid onnpoints, while ifnexceedsrit is a connected matroid of rankr. Moreover, the connectivity can be strengthened under additional hypotheses on the growth ofnandr, using the notion of vertical connectivity; and the values ofkfor which circuits of sizekexist can be determined in terms ofnandr

ISSN:0022-2526    

DOI:10.1002/sapm1984713181

年代:1984

数据来源: WILEY

摘要:

A construction of superantichains in the lattice of partitions of finite sets is presented that works for set sizes above 107. The construction refines Canfield's, which worked only for set sizes above 1020, and provides a classification of the properties of partitions which allow such antichains to exist.

ISSN:0022-2526    

DOI:10.1002/sapm1984713207

年代:1984

数据来源: WILEY

摘要:

A formal solution of the inverse scattering problem for then‐dimensional; time‐dependent and time‐independent Schrödinger equations is given. Equations are found for reconstructing the potential from scattering data purely by quadratures. The solution also helps elucidate the problem of characterizing admissible scatterin

ISSN:0022-2526    

DOI:10.1002/sapm1984713243

年代:1984

数据来源: WILEY

摘要:

A method for solving the inverse problem for a class of multidimensional first‐order systems is given. The analysis yields equations which the scattering data must satisfy; these equations are natural candidates for characterizing admissible scattering data. The results are used to solve the multidimensionalN‐wave resonant interaction equati

ISSN:0022-2526    

DOI:10.1002/sapm1984713251

年代:1984

数据来源: WILEY

摘要:

LetS,Tbe finite sets, and letfbe a function fromStoT. Fix an elementtinT, and letcndenote the number ofn‐tuples (X1,…,Xn) satisfyingf(X1) + … +f(Xn) =there + denotes any binary operation onT. The sequencec1,c2,… satisfies a linear recurrence relation of degree at m

ISSN:0022-2526    

DOI:10.1002/sapm1984713263

年代:1984

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1984713269

年代:1984

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1984713271

年代:1984

数据来源: WILEY