... 90C46
Abstract
We consider the problem to decomp ose a binary matrix into a small number of
binary matrices whose 1-entries form a r ectangle. We show that the linear relaxation
of this problem has an ... points on the vertical line
the electronic journal of combinatorics 16 (2009), #R89 12
A dual of the rectangle-segmentation problem
for binary...
... Introduction
The notion of variational bicomplexes was introduced in studying the problem
of characterizing the kernel and image of Euler-Lagrange mapping in the calcu-
lus of variations. This problem has ... variational bicom-
plexes have made an important role in many problems in caculus of variations
on manifolds, in diffrential geometry, in the theory of differenti...
... the form of a
“three-term recurrence”
σ (A
1
+ A
2
)σ (A
1
− A
2
)σ (A
4
+ A
3
)σ (A
4
− A
3
)=σ (A
4
+ A
1
)σ (A
4
− A
1
)σ (A
3
+ A
2
)σ (A
3
− A
2
)
−σ (A
3
+ A
1
)σ (A
3
− A
1
)σ (A
4
+ A
2
)σ (A
4
− A
2
),(5)
where
y ... u
i
,v
j
and e are arbitrary parameters on the elliptic curve.
First, we prove a lemma (set a = b = 0 to get the result...
... Molina
Department of Mathematics and Computer Science
Alma College
614 W. Superior St.
Alma MI, 48801
molina@alma.edu
Ken W. Smith
Department of Mathematics
Central Michigan University
Mt. Pleasant, ... A Proof of the Two-path Conjecture
Herbert Fleischner
Institute of Discrete Mathematics
Austrian Academy of Sciences
Sonnenfelsgasse 19
A- 1010 Vienna
Austria, EU
herbert.fleisch...
... dominant
principle.
Corollary 3.3. Assume that u and v are as in Theorem 3.1 and (dd
c
u)
n
≤
(dd
c
v)
n
.Thenu ≥ v.
4.ProofoftheMainTheorem
(i) We can assume v ≤ 0. Since (dd
c
v)
n
vanishes on every pluripolar set ... ∈
E
p
+ B
a
loc
which satisfying fdλ ≤ (dd
c
u)
n
.
For the definitions of
E
p
+ B
a
loc
and
F
p
+ B
a
loc
see Sec. 2.
Note that the main theorem for the...
... short for ‘standard Young
tableau’.)
Proof. Since the formula and all other things that are needed are stated uniformly
for the ordinary and shifted case, also the proof can be formulated uniformly, ... and a partition τ with at most n parts,
and finally mapping the partition τ to its conjugate π, thus obtaining the pair (Y,π)
consisting of the standard Young tableau Y and...
... 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 Tetali [6] show that bounds on the ... =
2
∆−2
.)
Before stating our main theorem we formally define the Markov chain for the Glauber
dynamics. For the purposes of the proof, the chain is defined on the s...
... of the finite general linear group GL
n
(q). The polynomial f
λ
(q) can be computed as the
generating function for the major index maj(T ) on the set of standard Young tableaux
of shape λ, ... Jackson, Combinatorial Enumeration, Dover Publications, 2004.
[5] K. Killpatrick, A Combinatorial Proof of a Recursion for the q-Kostka Polynomials,
Journal of Combinatorial...
... determinant evaluations and the Macdonald
identities for a ne root systems, Compositio Math. 142 (2006), 937-961.
[30] D. Stanton, Sign variations of the Macdonald identities, SIAM. J. Math. Annal.
17(1986), ... Guo and J. Zeng, Short proofs of summation and transformation formulas
for basic hypergeometric series, J. Math. Anal. Appl. 327:1 (2007), 310-325.
[21] M. D. Hirschhorn,...
... Ω.
In the case that the maximal subgroup G
e
of the minimal ideal is trivial and the action
of M on Ω is transitive, one has that each element of I(M) acts as a constant map and
Ω
∼
=
eM. This fact ... dimensional algebras
by analogy with semisimple algebras. In fact, the analogy between finite transformation
monoids and finite dimensional algebras is quite apt, as the theor...