... introduction.
One naturally wonders at the relationship of Dist to more familiar classes such as
NP and coNP. In this direction, applying the machinery of [6], we can argue that it is
unlikely that ... L
∈
Σ
P
k
.Above,
the notation
·
,
·
refers to some canonical pairing function. With these definitions,
NP = Σ
P
1
,coNP=Π
P
1
,andtheclassesΣ
P
k
and Π
P
k
form a neat hierarc...
... unknown.
The purpose of this article is to study and establish the ASCLT for self-normalized partial sums of random variables
in the domain of attraction of the normal law, we will show that the ASCLT ... article as it appeared upon acceptance. Fully formatted
PDF and full text (HTML) versions will be made available soon.
A note on the almost sure limit theorem f...
... A Note on the Symmetric Powers of the Standard
Representation of S
n
David Savitt
1
Department of Mathematics, Harvard University
Cambridge, MA 02138, USA
dsavitt@math.harvard.edu
Richard ... essentially what we are looking at. (The defining representation of S
n
consists of the direct sum of the reflection representation and the trivial representa-
tion. This tri...
... sharp estimates obtained by Kamath et al.
of the probability that no bin is empty after the random placement of the balls
and exploiting the relationship between the placement of balls and the rigid ... maximum.
A note on the non-colorability threshold of
a random graph
Alexis C. Kaporis, Lefteris M. Kirousis, and Yannis C. Stamatiou
University of Patra...
... depend on n. There are other applications of b-tries
in computer science, communications and biology. Among these are partial match retrieval
of multidimensional data, searching and sorting, pattern ... fixed large b and n, the conditions under which (c)–(e) apply may not
be satisfied for any k. However, for a fixed large b and k, we can always find a range of n
such that ea...
... A note on the ranks of set-inclusion matrices
D. de Caen
Department of Mathematics and Statistics
Queen’s University
Kingston, Ontario, Canada K7L 3N6
decaen@mast.queensu.ca
Submitted: ... be the (0,1)-matrix of inclusions
for t-subsets versus k-subsets of X : W
T,K
=1ifT is contained in K, and 0 otherwise.
These matrices play a significant part in several combinatorial...
... Background
Consider a Markov chain (P, Ω,π)whereP denotes the transition matrix, Ω denotes the
state space, and π denotes the unique stationary distribution. Recall that the variation
distance between ... with an extra slide-type move). They prove O(n log n) mixing time
of their dynamics for the same range of λ for all graphs. Dyer and Greenhill [3] and
Randall and Tet...
... C
4
contains v
∗
as a vertex, we must have that every w ∈ A appears in at
least one of A
−
or A
+
(it may appear in both; in particular, v
∗
appears in both A
−
and A
+
as there are no antiparallel ... this paper we consider the
most basic Tur´an-type problem in bipartite digraphs, namely, specifying conditions on the
cardinality of the edge-set of the digraph th...