Báo cáo toán hoc:"Locally Restricted Compositions II General Restrictions and Infinite Matrices" pptx
Báo cáo toán hoc:"Locally Restricted Compositions II. General Restrictions and Infinite Matrices" pptx
... locally restricted class
and Φ has span and modulus m.
(i) (R2) is equivalent to the gcd of the cycle lengths being 1.
(ii) If (R3) is true for k and k
′
> k, then it is true for k
′
.
(iii) For ... of (i) and (ii) are straightforward using the Cauchy-Schwartz inequality.
For (iii), let T
n
agree with T in the upper left n×n corner, and be zero elsewhere. Clearly,
(T −T
n
) ∈...
Báo cáo toán học: "Locally Restricted Compositions" doc
... E. Andrews, The Rogers-Ramanujan reciprocal and Minc’s partition function,
Pacific J. of Mathematics 95 (1981) 251–256.
[2] E.A. Bender and E.R. Canfield, Locally restricted compositions II: General ... Hitczenko and Stengle [8] and Hwang and Yeh [9]. A historical discussion
and various results are given by Hitczenko and Louchard [7].
Example 2 (Carlitz compositions) When...
Báo cáo toán học: "Locally Restricted Compositions III. Adjacent-Part Periodic Inequalitie" docx
... Bender and E.R. Canfield, Locally restricted compo sitions I. Restricted adjacent
differences, Elec. J. Combin. 12(1) (2005) R57, 27pp.
[3] E.A. Bender and E.R. Canfield, Locally restricted compositions ... ositions have m = 1 and c
i
= c
i+1
.
Strictly alternating compositions have m = 2 and c
i
< c
i+1
> c
i+2
.
In [3] we studied the general case of locally restrict...
Báo cáo toán học: "Words restricted by patterns with at most 2 distinct letters" pptx
... pattern -restricted sets that appeared in
our original paper (herein referred to as [BM]) and was also referred to in
S. Heubach, T. Mansour, Avoiding patterns of length three in compositions and ... i
2
= n + 1), and since α avoids 212 we have that
α
a
, α
b
are different for all a < i
1
< b < i
2
. Therefore, α avoids {112, 212} if and only if
(α
1
, . . ., α
i
1
−1
), a...
Báo cáo toán học: " The order dimension of Bruhat order on infinite Coxeter groups" potx
... Coxeter system and let v, w ∈ W . Then
(i) v ≤ w if and only if for every s ∈ S we have
s
v ≤
s
w.
(ii) v ≤ w if and only if for every s ∈ S we have v
s
≤ w
s
.
(iii) v ≤ w if and only if ... l(xy)=l(x)+l(y) and l(uv)=l(u)+l(v).
Then uv ≤ xy.
Proposition 4.2. If u, w ∈ W and s ∈ S have w>wsand u>us, then the following
are equivalent:
(i) w ≥ u
(ii) w ≥ us
(iii) ws...
Báo cáo toán học: "A Fixed Point Theorem for Nonexpansive Mappings in Locally Convex Spaces" ppt
... (H))) ⊂ T (H) ⊂ co(T (H)). Thus coT (H) ∈F. From this and
the minimality of H we get
coT (H)=H and hence
p
o
(Tz− x) ≤ r, ∀x ∈ H.
So Tz ∈ D,andT (D) ⊂ D. Hence D ∈F. By the minimality of H in F,
we ... exist λ ∈ (0, 1) and x, y ∈ X such
that
p
λ
(Tx− Ty) >p
λ
(x − y).
Putting t
o
= p
λ
(Tx− Ty)wehavep
λ
(x − y) <t
o
, and by (2), F
x−y
(t
o
) > 1 − λ.
On the other hand, it fo...
Báo cáo toán học: "Shift-Induced Dynamical Systems on Partitions and Compositions Brian Hopkins" pps
... components of size
15 and 7. For 12 and 13, the splits are 77 = 45 + 32 and 101 = 67 + 34, respectively.
The problem appears no easier for compositions: D
C
splits the 128 compositions in C(8)
into ... 1
21111
123
132
11112
11121
11211
12111
21111
Figure 6: Expanding the directed graph for the shift map on partitions of 6 to the map
on compositions of 6.
Results for compositions...
Báo cáo toán hoc:" Locally primitive normal Cayley graphs of metacyclic groups" potx
... nonabelian metacyclic group, and
ˆ
G < X 6
Aut(Γ ). Then n = 2 and G
∼
=
D
2m
is a dihedral group.
Proof. By Lemma 2.2, S = G, and all elements of S are involutions and conjugate under
Aut(G, ... that d 6 m/2.
Since r
2
≡ 1(mod m), and m is even, it follows r is o dd, and then 4|m. For each
σ ∈ Aut(G) and c ∈ G, it is easy to verify σ(c
2
) ∈ a, and then σ(a
m/2
) ∈ a...
Báo cáo toán học: "On restricted unitary Cayley graphs and symplectic transformations modulo n" docx
... > 0 odd and r ∈ Z
n
, we ha v e S
n
(r) = 0 if and only if at least one of
the followin g conditions hold:
(i) n is a multiple of 3, and r ≡ 2 (mod 3 );
(ii) n is a multiple of 5, and r ≡ ±1 ... N and M.
the electronic journal of combinatorics 17 (2010), #R69 12
Corollary 4-1. diam(G
p
m
) 2 for p an odd prime and m > 0; this inequality is strict if
and only if p ≡ 3 (...
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