37,890 research outputs found
Some aspects of (r,k)-parking functions
An \emph{-parking function} of length may be defined as a sequence
of positive integers whose increasing rearrangement
satisfies . The case
corresponds to ordinary parking functions. We develop numerous properties of
-parking functions. In particular, if denotes the
Frobenius characteristic of the action of the symmetric group
on the set of all -parking functions of length , then we find a
combinatorial interpretation of the coefficients of the power series for any . When ,
this power series is just ; when , we
obtain a dual to -parking functions. We also give a -analogue of this
result. For fixed , we can use the symmetric functions to
define a multiplicative basis for the ring of symmetric functions. We
investigate some of the properties of this basis
A useful variant of the Davis--Kahan theorem for statisticians
The Davis--Kahan theorem is used in the analysis of many statistical
procedures to bound the distance between subspaces spanned by population
eigenvectors and their sample versions. It relies on an eigenvalue separation
condition between certain relevant population and sample eigenvalues. We
present a variant of this result that depends only on a population eigenvalue
separation condition, making it more natural and convenient for direct
application in statistical contexts, and improving the bounds in some cases. We
also provide an extension to situations where the matrices under study may be
asymmetric or even non-square, and where interest is in the distance between
subspaces spanned by corresponding singular vectors.Comment: 12 page
The lightest neutral hypernuclei with strangeness -1 and -2
Our current knowledge of the baryon--baryon interaction suggests that the
dineutron and its strange analogue are unstable. In
contrast, the situation is more favorable for the strange three-body system
, and even better for the four-body system with strangeness , which is likely to be stable
under spontaneous dissociation. The recent models of the hyperon-nucleon and
hyperon-hyperon interactions suggest that the stability of the
and is possible within the uncertainties of our knowledge of the
baryon-baryon interactions. This new nucleus could be produced and
identified in central deuteron--deuteron collisions via reaction , and the tetrabaryon could play an important role in catalyzing
the formation of a strange core in neutron stars.Comment: Revised version accepted by PR
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