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1.
Letn>1. The number of all strictly increasing selfmappings of a 2n-element crown is
. The number of all order-preserving selfmappings of a 2n-element crown is
相似文献
2.
Christian Krattenthaler 《Monatshefte für Mathematik》1989,107(4):333-339
We give a combinatorial proof that
is a polynomial inq with nonnegative coefficients for nonnegative integersa, b, k, l withab andlk. In particular, fora=b=n andl=k, this implies theq-log-concavity of the Gaussian binomial coefficients
, which was conjectured byButler (Proc. Amer. Math. Soc. 101 (1987), 771–775). 相似文献
3.
Anastasios D. Simalarides 《Periodica Mathematica Hungarica》2000,40(1):71-75
Let be a primitive character mod k, k > 2. In [1], the following elementary estimate
4.
In this paper we show that if X is an s-distance set in
m
and X is on
p concentric spheres then
Moreover if
X is antipodal, then
. 相似文献
5.
In this paper, we consider the stochastic Dirac operatoron a polish space (Ω,β, P). The relation between the Lyapunov index, rotation number andthe spectrum of L_ω is discussed. The existence of the Lyapunov index and rotation number isshown. By using the W-T functions and W-function we prove the theorems for L_ω as in Kotani[1], [2] for Schrodinger operatorB, and in Johnson [5] for Dirac operators on compact space. 相似文献
6.
Richard P. Stanley 《Graphs and Combinatorics》1987,3(1):55-66
I. Bárány and L. Lovász [Acta Math. Acad. Sci. Hung.40, 323–329 (1982)] showed that ad-dimensional centrally-symmetric simplicial polytopeP has at least 2
d
facets, and conjectured a lower bound for the numberf
i
ofi-dimensional faces ofP in terms ofd and the numberf
0 =2n of vertices. Define integers
A. Björner conjectured (unpublished) that
(which generalizes the result of Bárány-Lovász sincef
d–1
= h
i
), and more strongly that
, which is easily seen to imply the conjecture of Bárány-Lovász. In this paper the conjectures of Björner are proved.Partially supported by NSF grant MCS-8104855. The research was performed when the author was a Sherman Fairchild Distinguished Scholar at Caltech. 相似文献
7.
Chang Jen-Chun Chen Rong-Jaye Hwang Frank K. 《Methodology and Computing in Applied Probability》2001,3(4):379-386
A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's
algorithm published in 1997, where
. In this paper we use automata theory to reduce
to
. For d small or close to k, we have reduced
from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is
, where
. 相似文献
8.
Nikolaos Marmaridis 《manuscripta mathematica》1984,47(1-3):55-83
Let
be a triangular matrix algebra, uhere k is an algebraically closed field, B is the path algebra of an oriented Dynkin diagram of type E6 or E7 or E8 and M is a finite dimensional k-B-bimodule. The aim of this paper is to determine the representation type of A for any orientation of the Dynkin diagram and for any indecomposable B-module M. This classification is obtained by comparing the representation types of the algebras
and
using the theory of tilting modules. 相似文献
9.
In the solution of the monotone variational inequality problem VI(, F), with
10.
И. Н. Пак 《Analysis Mathematica》1990,16(1):57-64
We generalize and sharpen certain results concerning Fourier series from the Lipschitz class. In particular, for
sinnx we prove the following: Let ¦bn¦n–2L(n) where L(x) is a continuous and slowly oscillating function. Then
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