... 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 ... systems
on 15 points. Recently, two algebraic invariants have been proposed to clas-
sify them. Let V denote the 35 block vectors v
i
of length 15 and hamming
weight 3 of such a sys...
... 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...
... B),
r
A
=min
λ∈C
σ
min
(A
∗
−λI)K
B
,
r
B
=min
λ∈σ(A)
σ
min
(B
∗
K
λ
),
where K
B
and K
λ
are the matrices representing KerB and Ker(A
∗
− λI), and
the formula of r
AB
is the result obtained in [4].
By the definitions, it is clear that r
AB
≤ min{r
A
,r
B
}, and the ... end of Sec. 3. And we also answer for the
498 D. C. Khanh and D. D. X. Thanh
The stabilizability radii of sys...