Báo cáo toán học: "Mr Paint and Mrs Correct" pot
Báo cáo toán học: "Codes, Lattices, and Steiner Systems" potx
... explicit determination of root systems
and lattices involved.
5 Acknowledgements
We thank Ed Assmus, Michel Deza, and Vladimir Tonchev for sending us
their preprints and Chris Charnes, Slava Grishukhin ... paper R9. J.H. Conway , N.J.A. Sloane,
Sphere Packings Lattices and Groups
[SPLAG] J.H. Conway, N.J.A. Sloane, Sphere Packings Lattices and Groups,
second edition, Springer Verlag...
Báo cáo toán học: "Tournament Sequences and Meeussen Sequences" pot
... name “random knock-out
tournaments.” A sequence (t
1
, ,t
n
) represented a tournament of n rounds beginning
with 1 +
t
i
players; in the first round 2t
n
players are paired off randomly and the ... the two trees, and therefore a unique bijection between tournament sequences
and Meeussen sequences which respects the ideas of extending or truncating a sequence.
To better understand Meeus...
Báo cáo toán học: "Continued fractions and Catalan problems" pot
... pattern and that T is among the smallest such
trees. We let v
3
be a vertex in T that provides the 3 in such a pattern and let v
1
,v
2
be the
vertices that provide the corresponding 1 and 2, ... 4
2 Lattice paths and ordered trees
We draw our ordered trees with the root at the top and proceed downward to the leaves.
The first leaf is the leftmost leaf in the drawing and the remain...
Báo cáo toán học: "Parking Functions and Noncrossing Partitions" pot
... poset of rank n with
ˆ
0and
ˆ
1 and with rank function ρ. (See [29,
Ch. 3] for poset terminology and notation used here.) Let S be a subset of
[n − 1] = {1, 2, ,n−1}, and define α
P
(S)tobethenumberofchains
ˆ
0=
t
0
<t
1
<··· ... a<b<c<dand some block B of π contains
both a and c,whilesomeblockB
of π contains both b and d,thenB=
B
. We establish some connections...
Báo cáo toán học: " Inclusion-Exclusion and Network Reliability" pot
... |X|≥k. Note that the minpaths and mincuts of (E,φ)are
the k-subsets and (n − k + 1)-subsets of E, respectively.
Now, let E be totally ordered, and for k-subsets X and Y of E define
X Y :⇔ x ≤ ... network and
φ(X) = 1 if and only if X contains the edges of an s, t-path. For source-to-T -terminal
reliability we take Σ = (E,φ), where E is the edge-set of the network and φ(X)=1
if...
Báo cáo toán học: "Schur functions and alternating sums" potx
... transposing
theentries 0and1 atindices 1and2 of(µ + α)[ ] or by transposing the entries −2
and −3 at indices 3 and 4. The result can be written as (4, 3, 3, 2, 2)[ ] respectively
as (4, 2, 4, 1, 3)[ ], and indeed ... Corollary. For λ, µ ∈Pand α ∈C, the Kostka number K
λ/µ,α
equals the
number # SST(λ/µ, α) of semistandard tableaux of shape λ/µ and weight α ,and
K
λ/µ,α
is the number...
Báo cáo toán học: "Noncrossing Trees and Noncrossing Graphs" pot
... within the circle and do not
cross each other. Noncrossing trees have been studied by Deutsch, Feretic and Noy [2],
Deutsch and Noy [3], Flajolet and Noy [4], Noy [6], Panholzer and Prodinger [7]. ... ··· ,C
r
and C
1
,C
2
, ··· ,C
r
are the cycles encountered in the edge deletion procedures for T and
T
.Since(i
1
,i
2
) /∈ E(T ), we may assume that (i
1
,i
2
) ∈ E(C
j
)...
Báo cáo toán học: "Edit distance and its computation" pot
... ∪
.
VB(K) and the edges are partitioned
E(K) = EW(K) ∪
.
EG(K) ∪
.
EB(K). The sets VW and VB are the white and black
vertices, respectively, and the sets EW, EG and EB are the white, gray and black ... of graphs. The theorems of Erd˝os and Stone [15] and
Erd˝os and Simonovits [14] give that
d
∗
(M) = 1/r, where r = min{χ(F ) − 1 : F ∈ M} and p
∗
(M) = 1.
Alon and Stav,...
Báo cáo toán học: " The structural and optical properties of GaSb/InGaAs type- quantum dots grown on InP (100) substrate" ppt
... measurements, and drafted the
manuscript. CY conducted the STEM measurement. SZ, TH, and GH conducted the
MBE growth. JH, WW, and CH coordinated the study. WL provided the idea and
conceived ... identified as the indirect transition from the
InGaAs conduction band to the GaSb hole level (type-II) and the GaSb QDs direct
interband transition (type-I) respectively, as shown in Fi...