... THE TYPICAL SET PARTITIONS MEET AND JOIN.
Boris Pittel
Received: May 16, 1999; Accepted: January 15, 2000
The lattice of the set partitions of [n] ordered by refinement is studied.
Suppose r partitions ... is the size of the largest block of p
typically? The answer is: two. And how
many two-elements sets are there in p
? The answer is: only about log
2
n/2....
... preparation and
analyses, and drafted the manuscript. Edward C. Norton and Shoou-Yih Lee
participated in the study design and helped to draft the manuscript. All
authors read and approved the final ... =
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OBBIRTH2004,NI
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If the inducement hypothesis held, the inducement
effect was expected to be posit...
... study the continuity of Julia set of some rational maps and the stability
of the Hausdorff dimension of the Julia set of polynomials
z
d
+ c (d ≥ 2)forsome
semi-hyperbolic parameters
c in the boundary ... x ∈ K meets all but finitely many K
n
;and
(2) If every neighborhood of x meets infinitely many K
n
,thenx ∈ K.
We define lim inf K
n
as the largest set satisfying (1), an...
... where A(G) is the adjacency matrix of G. Then
χ(G)=3 2and
the electronic journal of combinatorics 4 (1997), #R19 3
and
α(G) < min{ rank(B) |B ∈B(G)}
by theorem.
Acknowledgement.
The author is ... Gr¨otschel, L´aszl´oLov´asz, and Alexander Schrijver, Geometric Algorithms and Combina-
torial Optimization (Springer-Verlag, 1988).
3. Donald E.Knuth, The Sandwich Theorem”, Electro...
... selecting one of the m positions for a
(the vertices in [a, n], the gaps between
them, and the space after n) and one of the two positions for n
(n and the space after
n). All these 2m −3 choices ... get the series G and then equation (22). The radius of
convergence is the least positive root of the denominator.
Using the last theorem and the inequalities...
... vertices in V , and assign label x
to the smallest vertex. The condition (x, x
) ∈ F uniquely identifies vertex x
,andthe
labeling of the other vertices in the cycle C follows.
Removing the three ... (minimality
of x fixes the orientation of the edge), and that the choice of (x, x
) combined with the
information provided by the sequence completely determines the...
... the definition of the f
B
.NowtheP
i
and
B
j
form a symmetric tactical decomposition of the tactical configuration whose points are
the points of Σ
n−1
and whose blocks are the elements of B. Therefore ... the (d−1)-flats is similar to the action
of a n-cycle of the symmetric group on n elements on the set of d-element subsets.
Lemma 2.2 The G-stabilizer of any (d −1)-fl...
... by partitions in the set Λ
k
n
,
and the irreducible representations of CA
k+
1
2
(n) are indexed by partitions in the set Λ
k
n−1
.
Using the Schur-Weyl duality between S
n
and CA
k
(n)wegettheidentity
n
k
=
λ∈Λ
k
n
f
λ
m
λ
k
, ... is the left endpoint of the edge labeled j in d if and only
if j is the left endpoint of the edge labeled i in flip(d). Thus the...