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1.
Sara C. Billey William Jockusch Richard P. Stanley 《Journal of Algebraic Combinatorics》1993,2(4):345-374
Schubert polynomials were introduced by Bernstein et al. and Demazure, and were extensively developed by Lascoux, Schützenberger, Macdonald, and others. We give an explicit combinatorial interpretation of the Schubert polynomial
in terms of the reduced decompositions of the permutation w. Using this result, a variation of Schensted's correspondence due to Edelman and Greene allows one to associate in a natural way a certain set
of tableaux with w, each tableau contributing a single term to
. This correspondence leads to many problems and conjectures, whose interrelation is investigated. In Section 2 we consider permutations with no decreasing subsequence of length three (or 321-avoiding permutations). We show for such permutations that
is a flag skew Schur function. In Section 3 we use this result to obtain some interesting properties of the rational function
, where
denotes a skew Schur function.Sara C. Billey: Supported by the National Physical Science Consortium. William Jockusch: Supported by an NSF Graduate Fellowship. Richard P. Stanley: Partially supported by NSF grants DMS-8901834 and DMS-9206374 相似文献
2.
We obtain the decomposition of the tensor space
as a module for
, find an explicit formula for the multiplicities of its irreducible summands, and (when n 2k) describe the centralizer algebra
=
(
) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of
is given by the number of derangements of a set of 2k elements. 相似文献
3.
Itaru Terada 《Journal of Algebraic Combinatorics》2001,14(3):229-267
We interpret geometrically a variant of the Robinson-Schensted correspondence which links Brauer diagrams with updown tableaux, in the spirit of Steinberg's result [32] on the original Robinson-Schensted correspondence. Our result uses the variety of all
where
is a complete flag in
is a nondegenerate alternating bilinear form on
and N is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both and
instead of Steinberg's variety of
where
are two complete flags in
and N is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both
. 相似文献
4.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献
5.
Christiane Takacs 《Journal of Theoretical Probability》2001,14(3):699-715
We consider a random walk on
in a stationary and ergodic random environment, whose states are called types of the vertices of
. We find conditions for which the speed of the random walk is positive. In the case of a Markov chain environment with finitely many states, we give an explicit formula for the speed and for the asymptotic proportion of time spent at vertices of a certain type. Using these results, we compare the speed of random walks on
in environments of varying randomness. 相似文献
6.
Let
= {a
1, a
2,...} be a set of positive integers and let p
(n) and q
(n) denote the number of partitions of n into a's, resp. distinct a's. In an earlier paper the authors studied large values of log(max (2,p
(n)))/log(max(2,q
(n))). In this paper the small values of the same quotient are studied. 相似文献
7.
Sheila Sundaram 《Journal of Algebraic Combinatorics》1995,4(1):69-92
Let
denote the subposet obtained by selecting even ranks in the partition lattice
. We show that the homology of
has dimension
, where
is the tangent number. It is thus an integral multiple of both the Genocchi number and an André or simsun number. Using the general theory of rank-selected homology representations developed in [22], we show that, for the special case of
, the character of the symmetric group S
2n
on the homology is supported on the set of involutions. Our proof techniques lead to the discovery of a family of integers b
i(n), 2 i n, defined recursively. We conjecture that, for the full automorphism group S
2n, the homology is a sum of permutation modules induced from Young subgroups of the form
, with nonnegative integer multiplicity b
i(n). The nonnegativity of the integers b
i(n) would imply the existence of new refinements, into sums of powers of 2, of the tangent number and the André or simsun number a
n(2n).Similarly, the restriction of this homology module to S
2n–1 yields a family of integers d
i(n), 1 i n – 1, such that the numbers 2–i
d
i(n) refine the Genocchi number G
2n
. We conjecture that 2–i
d
i(n) is a positive integer for all i.Finally, we present a recursive algorithm to generate a family of polynomials which encode the homology representations of the subposets obtained by selecting the top k ranks of
, 1 k n – 1. We conjecture that these are all permutation modules for S
2n
. 相似文献
8.
L. Yu. Cherednikova 《Mathematical Notes》2005,77(5-6):715-725
Suppose that
is a system of continuous subharmonic functions in the unit disk
and
is the class of holomorphic functions f in
such that log|f(z)| ≤ B
f
p
f
(z) + C
f
, z ∈
, where B
f
and C
f
are constants and p
f
∈
. We obtain sufficient conditions for a given number sequence Λ = { λn} ⊂
to be a subsequence of zeros of some nonzero holomorphic function from
, i.e., Λ is a nonuniqueness sequence for
.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova. 相似文献
9.
Patrick Headley 《Journal of Algebraic Combinatorics》1997,6(4):331-338
Let be an irreducible crystallographic rootsystem in a Euclidean space V, with + theset of positive roots. For ,
, let
be the hyperplane
. We define a set of hyperplanes
. This hyperplane arrangement is significant inthe study of the affine Weyl groups. In this paper it is shown that thePoincaré polynomial of
is
, where n is the rank of and h is the Coxeter number of the finiteCoxeter group corresponding to . 相似文献
10.
Hiroshi Suzuki 《Journal of Algebraic Combinatorics》1998,7(2):165-180
It is well known that imprimitive P-polynomial association schemes
with
are either bipartite or antipodal, i.e., intersection numbers satisfy either
for all
for all
. In this paper, we show that imprimitive
-polynomial association schemes
with
are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either
. 相似文献
11.
Alexander A. Ivanov 《Journal of Algebraic Combinatorics》1992,1(1):45-69
The sporadic simple group F
2 known as Fischer's Baby Monster acts flag-transitively on a rank 5 P-geometry
. P-geometries are geometries with string diagrams, all of whose nonempty edges except one are projective planes of order 2 and one terminal edge is the geometry of the Petersen graph. Let
be a flag-transitive P-geometry of rank 5. Suppose that each proper residue of
is isomorphic to the corresponding residue in
. We show that in this case
is isomorphic to
. This result realizes a step in classification of the flag-transitive P-geometries and also plays an important role in the characterization of the Fischer–Griess Monster in terms of its 2-local parabolic geometry. 相似文献
12.
In this work we obtain an asymptotic estimate for the expected number of maxima of the random algebraic polynomial
, where a
j (j=0, 1,...,n–1) are independent, normally distributed random variables with mean and variance one. It is shown that for nonzero , the expected number of maxima is asymptotic to
log n, when n is large. 相似文献
13.
We obtain precise large deviations for heavy-tailed random sums
, of independent random variables.
are nonnegative integer-valued random variables independent of r.v. (X
i
)i
N with distribution functions F
i. We assume that the average of right tails of distribution functions F
i is equivalent to some distribution function with regularly varying tail. An example with the Pareto law as the limit function is given. 相似文献
14.
Hiroshi Suzuki 《Journal of Algebraic Combinatorics》1998,7(2):181-196
It is well known that an association scheme
with
has at most two P-polynomial structures. The parametrical condition for an association scheme to have two P-polynomial structures is also known. In this paper, we give a similar result for Q-polynomial association schemes. In fact, if
, then we obtain exactly the same parametrical conditions for the dual intersection numbers or Krein parameters. 相似文献
15.
16.
Let S = x
1,...,x
n} be a finite subset of a partially ordered set P. Let f be an incidence function of P. Let
denote the n × n matrix having f evaluated at the meet
of x
i and x
j as its i, j-entry and
denote the n × n matrix having f evaluated at the join
of x
i and x
j as its i, j-entry. The set S is said to be meet-closed if
for all 1 i, j n. In this paper we get explicit combinatorial formulas for the determinants of matrices
and
on any meet-closed set S. We also obtain necessary and sufficient conditions for the matrices
and
on any meet-closed set S to be nonsingular. Finally, we give some number-theoretic applications. 相似文献
17.
Gerold Alsmeyer 《Journal of Theoretical Probability》2002,15(2):259-283
It is proved that for each random walk (S
n
)
n0 on
d
there exists a smallest measurable subgroup
of
d
, called minimal subgroup of (S
n
)
n0, such that P(S
n
)=1 for all n1.
can be defined as the set of all x
d
for which the difference of the time averages n
–1
n
k=1
P(S
k
) and n
–1
n
k=1
P(S
k
+x) converges to 0 in total variation norm as n. The related subgroup
* consisting of all x
d
for which lim
n P(S
n
)–P(S
n
+x)=0 is also considered and shown to be the minimal subgroup of the symmetrization of (S
n
)
n0. In the final section we consider quasi-invariance and admissible shifts of probability measures on
d
. The main result shows that, up to regular linear transformations, the only subgroups of
d
admitting a quasi-invariant measure are those of the form
1×...×
k
×
l–k
×{0}
d–l
, 0kld, with
1,...,
k
being countable subgroups of
. The proof is based on a result recently proved by Kharazishvili(3) which states no uncountable proper subgroup of
admits a quasi-invariant measure. 相似文献
18.
Introduce the notation:
, is the union of two segments [-1,1] and [-1 +
,1+
],
is a noninteger number,
is the Hölder class with exponent
on
The following result announced by the authors in [J. Math. Sci. 117 (2003), No. 3] is proved. There exist numbers a
1 (
) , b
1 (
)
0 depending only on
such that for any
there exists a polynomial
, such that
. Bibliography: 11 titles. 相似文献
19.
Hélène Barcelo 《Journal of Algebraic Combinatorics》1993,2(1):5-23
We describe a straightening algorithm for the action of S
n on a certain graded ring
. The ring
appears in the work of C. de Concini and C. Procesi [2] and T. Tanisaki [8], and more recently in the work of A. Garsia and C. Procesi [4]. This ring is a graded version of the permutation representation resulting from the action of S
n on the left cosets of a Young subgroup. As a corollary of our straightening algorithm we obtain a combinatorial proof of the fact that the top degree component of
affords the irreducible representation of S
n indexed by . 相似文献
20.
Vratislava Mošová 《Applications of Mathematics》2000,45(6):401-410
As a measure of deformation we can take the difference D
- R, where D
is the deformation gradient of the mapping
and R is the deformation gradient of the mapping
, which represents some proper rigid motion. In this article, the norm
is estimated by means of the scalar measure e(
) of nonlinear strain. First, the estimates are given for a deformation
W
1,p() satisfying the condition . Then we deduce the estimate in the case that
(x) is a bi-Lipschitzian deformation and . 相似文献