Báo cáo toán học: "Parking functions, empirical processes, and the width of rooted labeled trees" pps
Báo cáo toán học: "Parking functions, empirical processes, and the width of rooted labeled trees" pps
... motivations of Odlyzko and Wilf, when they study the width of labeled
trees, is to give a tight estimate for the average bandwidth of this class of tree.
2 The breadth first search random walk
From ... initially
(0). Then, at each of the n following stages of the BFS, the vertex x at the head of the
queue is removed from the queue, and all “new” neighbor...
Báo cáo toán học: "Parking Functions and Noncrossing Partitions" pot
... Λ(π
i−1
,π
i
)andminB
. It is easy to see that Γ
m
is a tree. Root Γ
m
at the
vertex 1 and erase the vertex labels. If v
i
is the vertex of e
i
farthest from the
root, then move the label i of the edge ... ,Λ(π
n−1
,π
n
)).
3.1 Theorem. The labels Λ(m) of the maximal chains of NC
n+1
consist of
the parking functions of length n,eachoccuringonce.
Proof. If Λ(π...
Báo cáo toán học: "Parking functions of types A and B" ppsx
... have the same number of elements. First
we remark that there is a natural action of S
n
on the set of parking functions, which
permutes the a
j
. There is also an action of S
n
on the set of factorizations, ... w].
If W = S
n
is the group of permutations of [1,n], then the reflections are the transposi-
tions, and w is the cycle (1 2 n). To any permutation σ ∈...
Báo cáo toán học: "Parking functions, stack-sortable permutations, and spaces of paths in the Johnson graph" docx
... arrive at the first element of p, p
k
. At this point, the top of the stack
is the index of the last element of q encountered. We move the top of the stack out, as
the first entry of the right ... arrive at the element p
s
of p, the top of the stack is the index of the
smallest element of q which is not smaller than p
s
, other than the elements...
Báo cáo toán học: "COMPOSITION SUM IDENTITIES RELATED TO THE DISTRIBUTION OF COORDINATE VALUES IN A DISCRETE SIMPLEX" pptx
... pictures of weight k.Acard of weight k
is a pair consisting of a picture of weight k and a k-element subset of N that we will call the
label set of the card. A hand of weight n and size l is a set of ... bijection between the set of compositions of n −2by{1, 2} and the
set of compositions of n − 1 by odd numbers. The bijection works by prepending a 1 to...
Báo cáo toán học: "Weakly Self-Avoiding Words and a Construction of Friedman" ppt
... self-avoiding
then we append q0andq1 to the end of the queue.
the electronic journal of combinatorics 8 (2001), #N2 2
Weakly Self-Avoiding Words and a Construction of
Friedman
Jeffrey Shallit
∗
and Ming-wei ... subword of “introduction”.
1
We use the notation x[k]todenotethek’th letter chosen from the string x. We write
x[a b] to denote the subword of x of length b...
Báo cáo toán học: "Weighted Aztec Diamond Graphs and the Weyl Character Formula" doc
... Given a matching m of
the Aztec diamond graph A, define the weight of the matching (m) to be the product
of the weights of all the edges in the matching. Then the weight of the Aztec graph A is
(A)=
m
(m), ... graph of order n is the dual graph to the Aztec diamond of order
n in which the vertices are the squares and an edge joins two vertices if...
Báo cáo toán học: " h∗-vectors, Eulerian polynomials and stable polytopes of graph" pdf
... faces of ∆ for 0 ≤ i ≤ d − 1andf
−1
=1. We
say that ∆ is a triangulation of a polytopal complex F if the union of the faces of ∆ is
equal to the union of the faces of F and every face of ∆ is ... from the description of the facets of
P that if I
0
⊂ I
1
⊂···⊂I
e
is a chain of nonempty ideals of Ω
0
as in the definition of the
ideal height for Ω then t...
Báo cáo toán học: "A note on polynomials and f -factors of graphs" docx
... |E|.
Theorem 1 can also be extended to hypergraphs, but the appropriate condition on |f(v)|
then depends on the upper rank of the hypergraph – that is, the size of the largest
hyperedge.
The proofs ... 1},
then F is the edge set of a non-trivial partial f-factor of G.
3 Concluding Remarks
We mention a possible direction for extending the results of Theorem 1 and Th...
Báo cáo toán học: "Chromatic Graphs, Ramsey Numbers and the Flexible Atom Conjecture" potx
... some
c ∈ R and realize the above as a quadratic polynomial in c. Since the coefficient of c
2
is
negative, the function is concave down. By finding the zeros of this polynomial in terms
of n and then ... B
m+
for m ≤ . Then by making superficial changes to the
remainder of the proof we establish the result for the nonsymmetric case. Thus we have
the following:
the...
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