Báo cáo toán học: "An Ehrhart Series Formula For Reflexive Polytopes" pptx
Báo cáo toán học: "An Ehrhart Series Formula For Reflexive Polytopes" pptx
... 1, and α
m
, β
n
≥ 0.
the electronic journal of combinatorics 13 (2006), #N15 4
An Ehrhart Series Formula For Reflexive Polytopes
Benjamin Braun
Department of Mathematics
Washington University, ... x)
d+1
denote the rational generating function for this polynomial (as in [7], chapter 4), called
the Ehrhart series of P . See [3] for more information regarding Ehrhart theory....
Báo cáo toán học: "An inverse matrix formula in the right-quantum algebra" ppt
... straightforward bookkeeping, cf. [KP07, §§5–8]. However, Theorems 5.3
and 6.1 do not seem to extend to a formula for general q or q
ij
.
As can be seen from the proof of Theorem 4.1, the formula
1
I ... height
j
k
can be before some of the steps with starting height i, σ
−1
(i) ≤ σ
−1
(j
k
).
For a q-sequence α, denote by ψ(α) the q-sequence we get by performing the switch
described...
Báo cáo toán học: "An improved tableau criterion for Bruhat order" ppt
... introduce a forbidden descent we must have j ≤ k<m.
Hence, x
j
<x
m
= y
j
,andx
i
= y
i
for i ∈{1, ,k}−{j}.
Conversely, suppose that x
i
≤ y
i
for all 1 ≤ i ≤ k,andthatx
j
<y
j
for some ... criterion, which is valid for all Coxeter groups.
1 Introduction
The classical tableau criterion for Bruhat order on
S
n
says that
x
≤
y
if and only if
x
i,k
≤
y
i,k
for all 1
≤
i
≤
k...
Báo cáo toán học: " AN EXACT PERFORMANCE BOUND FOR AN O(m + n) TIME GREEDY MATCHING PROCEDURE" pptx
... the
maximum possible size that can be guaranteed for the given values of n and m.
We can reformulate Theorem 3 to have fewer variables by explicitly solving for
k
max
. To do this we need two lemmas. ... Also,
b(n, r) = max(f(n, r),g(n, r)) when n ≥ 2 and r ≥ 1. (7)
4 Performance Guarantees
The following performance guarantee for the greedy matching procedure is the main
result of the p...
Báo cáo toán hoc:" An Edge-Minimization Problem for Regular Polygons " pps
... following:
Proposition 4 The smallest edge-sharing necklace for an n-gon is a
3-cycle for n ≡ 0 (mod 6)
4-cycle for n ≡ 2, 4 (mod 6)
6-cycle for n ≡ 1, 3, 5 (mod 6).
2.7 Classification of 4-cycle ... 1
f − 1
.
Therefore, maximizing f for fixed v is equivalent to minimizing e/(f − 1). In the next
subsection we will show that for each n there is a minimum length c
min
∈ {3,...
Báo cáo toán hoc:" An Elementary Chromatic Reduction for Gain Graphs and Special Hyperplane" pps
... particular,
χ
Z
S
n
(q) = (q − n + 1)
n
for q n − 1,
χ
mod
S
n
(q) = q(q − n)
n−1
for q > n,
χ
∗
S
n
(q) = q(q − n)
n−1
.
As we mentioned, the formula for χ
∗
S
n
(q) is already known from ... to the first formula of Lemma 3.2, we get
F (Γ
0
) =
S∈F(Γ
0
)
µ
0
(0, S)F ( ( Φ/S)\E
0
).
This is the theorem.
Homomorphic Proof of Theorem 4.3. Apply the same F to the second formula...
Báo cáo khoa học: "An exponential translation model for target language morphology" pptx
... number.
• For verbs, generated forms had to match the
original form for tense and negation.
• For adjectives, generated forms had to match
the original form for degree of comparison and
negation.
• For ... The forms pro-
duced by the tool from the lemma of an observed in-
flected word form were subjected to several restric-
tions:
• For nouns, generated forms had to match the
origi...
Báo cáo toán học: "New Lower Bound Formulas for Multicolored Ramsey Numbers" pptx
... Subject Classification: 05D10
Abstract
We give two lower bound formulas for multicolored Ramsey numbers. These formu-
las improve the bounds for several small multicolored Ramsey numbers.
1. INTRODUCTION
In ... INTRODUCTION
In this short article we give two new lower bound formulas for edgewise r-colored
Ramsey numbers, R(k
1
,k
2
, ,k
r
), r ≥ 3, defined below. Both formulas are derived...
Báo cáo toán học: "An elementary proof of the hook formula" ppt
... probabilistic proof of
a formula for the number of Young tableaux of a given shape. Adv. in Math.,
31(1):104–109, 1979.
[GT96] Adriano M. Garsia and Glenn Tesler. Plethystic formulas for Macdonald q, ... Acknowledgements
The author is grateful to Adriano Garsia for pointing out the q, t-analog of the hook
formula in [GT96]. This suggested that the recursion for the hook formula...