... 6
The asymptotic behavior of the average
L
p
−discrepancies and a randomized discrepancy
Stefan Steinerberger
∗
Department of Financial Mathematics, University of Linz
Altenbergstraße 69, A- 4040 ... imbalance, we make the interval slightly larger: We make a smaller
and b larger (remember that we are on the torus, making a smaller if a is already 0 means
rea...
... =3 )and( 6;m =1)
the electronic journal of combinatorics 7 (2000), #R50 11
References
[1] M. Abramowitz and I .A. Stegun, Eds., Handbook of Mathematical Functions with
Formulas, Graphs and Mathematical ... comments and
suggestions which have led to a substantially improved paper.
An Asymptotic Expansion for the Number of
Permutations with a Certain Number of Inversions...
... and topology and in other branches of mathematics and physics, such as Boole’s
algebra, operational researches, theory of algorithms and graphs, combinatorial analy-
sis, nuclear and astrophysics, ... fluxes and the
like. ED was primarily engaged in 2D and 3D graphics and visualization functions and their zeros and examining
many singularities. All of the previou...
... Generations of the
Rudvalis Group Ru
Ali Reza Ashrafi
1
and Ali Iranmanesh
2
1
Department of Mathematics, Faculty of Science,
University of Kashan, Kashan, Iran
2
Department of Mathematics, Tarbiat ... 6 Ali Reza Ashrafi and Ali Iranmanesh
Case 4. Ru is 7A- complementary generated. If pY ∈Athen by Table 1 and Ta-
ble 3, there is no maximal subgroup of Ru that contains (pY, 7...
... Everything below is phrased in terms of the
Riemann ξ-function, but the manipulations work equally well for any function such that it and all
of its derivatives have the same number of zeros. We write ... inequality (3) is not simultaneously sharp for all n, and this possibility
imparts some weakness to the result. A lower bound for N
d
(T) was calculated in [CGG] in a s...
... MA 02138, USA
cohn@math.harvard.edu
Dedicated to my grandparents Garnette Cohn (1907–1998) and Lee Cohn (1908–1998)
Abstract. We study the 2-adic behavior of the number of domino tilings of a ... Classification. 0 5A1 5, 1 1A0 7.
The author was supported by an NSF Graduate Research Fellowship.
1
the electronic journal of combinatorics 6 (1999), #R14 7
Proof. The proof i...
... loops are con-
sidered. Note that the iterated line graph of a path eventually becomes the empty
graph and that the iterated line graphs of cycles and K
1,3
(whose line graph is a tri-
angle) ... the maximum and minimum degree both have order Θ(2
k
).
Niepel, et al., have conjectured that the maximum degrees of all iterated line
graphs, with the exception of path...
... w
1
is a standard n
d
1
-variable matrix, w
2
is a standard n
d
2
-variable
matrix, and the space associated with w
1
is contained in the space associated with w
2
,
then we will say that w
1
is a ... r-cell partition of the standard n
d
-variable matrices over M
N
k
(d), there exists a
standard t
d
-variable matrix over M
N
k
(d) all of whose standard n
d
-variable submat...
... and treated in the
theses [10] and [15]. The PPC first appeared in the literature in 1983, in a paper by
Laborde, Payan and Xuong [11]. Although that paper dealt mainly with directed graphs,
they ... ( A ) ≤ a and
τ(B) ≤ b is called an (a, b)-partition of G.IfG has an (a, b)-partition for every pair (a, b)
of positive integers such that a + b = τ(G), then we say that...
... self-contained and completely elementary
proofs of the combinatorial interpretation and closed formulas for the Laurent polynomial
expressions of the elements x
m
and s
n
.
2 Results
We start by ... basis.
As a special case of the Laurent phenomenon established in [3], A is contained in
the Laurent polynomial ring Z[x
±1
1
, x
±1
2
]. In particular, all x
m
and s
n...