... properties of the set of the hook numbers for some special families of
(fixed) skew -Young diagrams (Theorem1.2). The problem appeared in the study of
the hook formula for various kinds of Young diagrams. ... problem
appeared in the study of the hook formula for various kinds of Young diagrams.
The proofs are based on properties of shifted Schur functions, due t...
... δ). We establish these values in
Sections 2, 3 and 4.
TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS
OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE
W. Edwin Clark
University of South Florida
Tampa, ... y.IfA⊆V then we let A denote the subgraph of G induced by A.
Table 1 contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value is
known, ot...
... of Connectedness
and the Distribution of Number of Components
Jason P. Bell
Department of Mathematics
University of California, San Diego
La Jolla, CA 92903-0112, USA
(email: jbell@math.ucsd.edu)
Edward ... depends on the type of map, and
A depends on both the type of map and the surface. See [22] for a proof of (7) for the
unrooted case an...
... associated with strips of Young diagrams, Adv. in Math.
41 (1981), 115–136.
ASYMPTOTICS OF THE NUMBER OF
k-WORDS WITH AN -DESCENT
Amitai Regev
∗
Department of Mathematics
The Pennsylvania State ... −1)!
Standard and Semistandard Tableaux.
Let λ n (i.e. λ is a partition of n). A tableau of shape λ, filled with 1, ···,n,
is standard if the numbers in it are in...
... graph of order n with
domination number at least 3 and minimum degree δ satisfying
n −2
√
n −4 ≤ δ ≤ n −
√
2
√
n.
Tight Upper Bounds for the Domination Numbers of
Graphs with Given Order and Minimum ... combinatorics 7 (2000), #R58 19
[2] W. Edwin Clark and Larry A. Dunning, Tight Upper Bounds for the Domination
Numbers of Graphs with...
... electronic journal of combinatorics 9 (2002), #R21 10
On counting permutations by pairs of congruence
classes of major index
H
´
el
`
ene Barcelo and Robert Maule Sheila Sundaram
Department of Mathematics ... give a constructive proof of an equivalent restatement of Propo-
sition 2.5, by looking at the circular classes of permutations τ ∈ S
n
which fix n. Not...
... behavior of f(n, p, q) between the linear and quadratic orders of
magnitude, so for q
lin
≤ q ≤ q
quad
. In particular we show that that we can have at most
log p values of q which give a linear ... denotes the parity of the natural
number n,soitis1ifn is odd and 0 otherwise.
1.2 Edge colorings with at least q colors in every subset of p
vertice...
... electronic journal of combinatorics 10 (2003), #R40 10
Asymptotics of Permutations with
Nearly Periodic Patterns of Rises and Falls
Edward A. Bender
Department of Mathematics
University of California, ... N
a
N
b
···N
z
.Equivalently,we
can work with T
−1
and thus deal with eigenfunctions of the differential operators N
−1
d
and N
−1
u
,whichared/dx and −d/...
... Bower
and Michael: if a d-dimensional rectangular box can be tiled using translates of two
types of rectangular bricks, then it can also be tiled in the following way. We can
cut the box across ... our box by translations. All rectangles that appear in this note are axis-aligned.
Bower and Michael [1] recently showed the following nice result. A hyperplane cut is a
separat...
... the proof of Lemma 2 in our
proof of Theorem 1, we will include the full proof of Lemma 2 there.
As examples of these lemmas, for the symmetric group, which has m = n(n − 1)/2
roots, the asymptotic ... covariance form
of X.LetY
N
be the sum of N independent copies of X. For any vector v,letp(v) be the
probability for the random walk, and let q(v) the...
... for example.
the electronic journal of combinatorics 14 (2007), #R37 9
A combinatorial representation with Schrăoder paths of
biorthogonality of Laurent biorthogonal polynomials
Shuhei Kamioka
∗
Department ... certain kinds of Schrăoder paths, which
imply orthogonality and biorthogonality of LBPs.
1 Introduction and preliminaries
Laurent biorthogonal polynomial...
... case of 2–
watermelons with a wall.
ã In appendix A, we summarize background information on
– Stirling’s approximation,
– certain residues and values of the gamma and zeta function,
– a certain ... journal of combinatorics 14 (2007), #R64 11
Asymptotics of the average height of 2watermelons
with a wall.
Markus Fulmek
Fakultăat făur Mathematik
Universităat Wien
N...
... weight of a piece
the electronic journal of combinatorics 15 (2008), #R76 17
A combinatorial derivation with Schrăoder paths of a
determinant representation of Laurent biorthogonal
polynomials
Shuhei ... interpretation [2] of Jacobi
type continued fractions (J-fractions), a combinatorial interpretation in terms of Motzkin
and Favard paths. Specifically h...
... X
u
)-DS of G. Hence, γ(G
u
; X
u
) ≤
|D
v
| + 1 = γ(G
v
; X
v
) + 1. ✷
the electronic journal of combinatorics 18 (2011), #P12 34
A new bound on the domination number of graphs
with minimum degree ... is of interest to determine upper
bounds on the domination number of a graph. In 1989, McCuaig and Shepherd [12]
presented the beautiful result that...
... 9:35
http://www.annals -general- psychiatry.com/content/9/1/35
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aripiprazole in a general outpatient psychiatric practice
setting and to evaluate the effectiveness of aripiprazole in
a Taiwanese patient ... effectiveness in the management of patients with
schizophrenia or schizoaffective disorder in a general psychiatric
out...