Báo cáo toán học: "Conjectured Statistics for the Higher q, t-Catalan Sequences" potx
Báo cáo toán học: "Conjectured Statistics for the Higher q, t-Catalan Sequences" potx
... of the higher q, t-Catalan sequences.
In the rest of the paper, we present some conjectured combinatorial interpretations for
the higher q, t-Catalan sequences. We prove some combinatorial formulas, ... proved for these trivariate sequences.
1 Introduction
In [7], Garsia and Haiman introduced a q, t-analogue of the Catalan numbers, which they
called the q, t-C...
Báo cáo toán học: " Some results for the q-Bernoulli, q-Euler numbers and polynomials" doc
... 10 of 16
Remark 3.2. The remarkable point is that the series on the right-hand side of Lemma
3.1 is uniformly convergent in the wider sense.
From (2.13)and (2.14), we define the q-Bernoulli and ... formulas for the q-Bernoulli and q-
Euler polynomials which will be used to prove the main results of this article.
In Section 4, we construct the q-analogue of the Riemann’s ζ-...
Báo cáo toán học: "Threshold Functions for the Bipartite Tur´n Property a" potx
... =0|z=n
2
p)≤P(X=0|z≤n
2
p)≤3P(X=0)→0
by the theorem, where the last inequality above follows due to the observation that
P(A|B) ≤ P(A)/P(B) and the fact that the central limit theorem [or the approxi-
mate and ... = o(n
1/3
); in the last two lines of the above calculation, the notation f g means that
f ≥ Kg for some positive constant K. This proves the theorem; as in...
Báo cáo toán học: "Improved bounds for the number of forests and acyclic orientations in the square lattice" doc
... several counting problems on
the square lattice L
n
. There the authors gave the following bounds for the asymp-
totics of f(n), the number of forests of L
n
,andα(n), the number of acyclic orienta-
tions ... proof gives the following
Theorem 6.13. Let 2 ≤ k ≤ 8, then
lim
n→∞
(α(F
k−1
n
))
1/n
= ρ(D
k
).
Finally, using Theorem 6.1 and Theorem 6.2 together with the last two...
Báo cáo toán học: "Lower Bound for the Size of Maximal Nontraceable Graphs." pot
... 10 has at least
3n−2
2
edges.
The first one concerns the lower bound for the number of edges of MNH graphs. It is the
combination of results proved in [2] and [7].
Theorem 1 (Bondy and Lin, Jiang, ... traceable for each
e ∈ E(
G).
∗
This material is based upon research for a thesis at the University of South Africa and is supported
by the National Research Foundation under Gr...
Báo cáo toán học: "Lower bounds for the football pool problem for 7 and 8 matches" pdf
... =
σ∈L
x
σ
for each L ∈ L,
the electronic journal of combinatorics 14 (2007), #R27 2
Lemma 4 a) If σ ∈ B
∗
1
, then there exists L ∈ L
≥5
(see (4)) with σ ∈ L.
b) If σ ∈ B
∗
2
, then either there ... 4 resp. k = 5). In the case n = 7 the best
previously known lower bound k
3
(7) ≥ 153 is due to Habsieger [5]. We show
Theorem 1. k
3
(7) ≥ 156.
For the case of 8 matches the best...
Báo cáo toán học: "Lower Bounds for the Size of Random Maximal H-Free Graphs" pdf
... holds for d − 1. We prove the claim for d. Let S = (G
1
, G
2
, . . . , G
d
)
be the sequence of the labels of the nodes u
i
, i ∈ [d], along the path P . Assume for the
sake of contradiction ... {f }∪
i<d
G
i
then by the observation made in the
previous paragraph we are done, since this implies that S is a bad sequence. Therefore, we
can assume for the rest of...
Báo cáo toán học: "Comultiplication rules for the double Schur functions and Cauchy identities" docx
... s
µ
(x
/y
||a),
implied by the combinatorial formula (2.14). Therefore, the required relation follows by
comparing the two expansions.
An explicit formula for the polynomials c
ν
λµ
(a) is provided by the following ... well as to an explicit formula for the c
ν
P, µ
(a) in terms of the values of P ; see [19].
Therefore, the (dual) Littlewood–Richardson polynomials a...
Báo cáo toán hoc:"Generating functions for the number of permutations with limited displacement." ppsx
... A
0
.
Moreover, we note that at the start of the i’th step, |{j < i | p
j
< p
i
}| columns to the
left of the column p
i
in the original A
0
have already been removed. Therefore, at the i’th
step, when ... det(I − zT )) = 1
for the second transfer-matrix method, and that the matrix in the second transfer-matrix
method is smallest possible for any transfer-matrix f...
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