Báo cáo toán học: "Matchings avoiding partial patterns and lattice paths" pps
Báo cáo toán học: "A generalization of dissipativity and positive semigroups " ppsx
... class="bi x0 y0 w3 h 1" alt =""
Báo cáo toán học: "Escher''''s Combinatorial Patterns" pot
... played the game with his father.) Two pieces of
cut potato can serve as the medium on which to carve the motif and its reflected image, and then
these potato stamps are inked and used to produce a ... translations of the
translation block. These symmetries add a geometric layer of complexity to the combinatorial
scheme.
Escher's Case (1)
We first consider Escher's case (1), in whi...
Báo cáo toán học: "Cycle index, weight enumerator, and Tutte polynomial" ppsx
... IBIS property holds.
the electronic journal of combinatorics 9 (2002), #N2 7
Cycle index, weight enumerator, and Tutte polynomial
Peter J. Cameron
School of Mathematical Sciences
Queen Mary, University ... the analogues of restriction and
contraction, and it specialises to the weight enumerators of each of the “elementary divisors”
of C (the two binary codes C mod 2 and (C...
Báo cáo toán học: "Words restricted by patterns with at most 2 distinct letters" pptx
... 33111 322 24 → 331 322 2411 → 331 324 221 1
→ 3431 322 211 → 3431 322 211 ∈ [4]
10
(1 12) .
(7)
the electronic journal of combinatorics 9 (2) (20 02) , #R3 15
Corollary 16 For any p ≥ 0
F
v
p,0
(x; 2) = e
x
p
j=0
x
j
j!
.
Proof. ... 121 }, {1 12, 121 }, {1 12, 122 }, {1 12, 21 1}, {1 12, 21 2}, {1 12, 22 1}, { 121 , 21 2}.
Theorem 5 The pairs {111, 1 12} and {111, 121 } are Wilf e...
Báo cáo toán học: "Permutations avoiding two patterns of length three" ppt
... work
of Mansour [14], who computed generating functions for the number of n-permutations
that avoid two distinct patterns of length three and contain exactly one copy of another
pattern of any length.
It ... avoid two distinct patterns of length three and any
additional set of patterns. We begin by showing how to enumerate these permuta-
tions using generating tre...
Báo cáo toán học: "Packing densities of patterns" ppsx
... symbol of σ.Sincen +1>m, we can select a random subsequence
of σ of length m by first throwing out one of the n + 1 symbols of σ at random and
then randomly selecting a subsequence of length ... the following theorem of
Stromquist. We give a proof which is somewhat shorter than the proof in [1], both
for its own interest and because we will reuse the method of proof when stu...
Báo cáo toán học: "Words avoiding a reflexive acyclic relation" doc
... Waterloo
Waterloo, Ontario CANADA N2L 3G1
ipgoulde@math.uwaterloo.ca
Curtis Greene
Department of Mathematics, Haverford College
Haverford, PA 19041
cgreene@haverford.edu
Dedicated to Richard Stanley ... a combinatorial explanation for (24) and (25). First, some notation.
Since A is defined by a tree, there is a unique (alternating) path between any pair of
distinct vertices. For a, b...
Báo cáo toán học: "Combinatorics of Partial Derivatives" pdf
... 2.
3 Proofs of the first two Propositions
Proof of Proposition 1. This proof relies on this simple standard algorithm for con-
verting a list of all partitions of { 1, ,n} into a list of all partitions ... partitions of { 1, ,n+1}:
1. To each partition of { 1, ,n}, add the 1-member-set { n +1} as a new block.
This gives a list of some of the partitions of { 1, ,n+1}.
2. To...
Báo cáo toán học: "Distribution of crossings, nestings and alignments of two edges in matchings and partitions" pot
... Crossing, nesting and alignments of two edges
The numbers of crossings, nestings and alignments of two edges in π will be denoted by
cr(π), ne(π)andal(π), respectively. For the partition π in Figure ... crossings and nestings of two edges in
matchings, preprint, math.CO/0510676, 2005.
[9] C. Krattenthaler, Growth diagrams, and increasing and decr...
Báo cáo toán học: "New regular partial difference sets and strongly regular graphs with parameters (96,20,4,4) and (96,19,2,4)" ppsx
... Algorithms, and Programming, Version
4.3; Aachen, St. Andrews (1999).
the electronic journal of combinatorics 13 (2006), #R88 10
New regular partial difference sets and strongly regular
graphs with parameters ... partial difference sets S
1
and S
2
in a group H, the graphs Cay(H, S
1
) and Cay(H, S
2
) can be isomorphic. Similarly, for
two inequivalent partia...
Báo cáo toán học: "Matchings avoiding partial patterns and lattice paths" pps
... this paper, we consider matchings avoiding partial patterns 1123 and 1132.
We give a bijection between 1123 -avoiding matchings with n edges and nonnegative
lattice paths from (0, 2) to (2n, 0). ... 1132 -avoiding
matchings with n edges and lattice paths from (0, 0) to (2n, 0) starting with an up step.
the electronic journal of combinatorics 13 (2006), #R89 2
Matchings avo...
Báo cáo toán học: "Matchings Avoiding Partial Patterns" ppsx
... 05A05, 05C30
Abstract
We show that matchings avoiding a certain partial pattern are counted by the 3-
Catalan numbers. We give a characterization of 12312 -avoiding matchings in terms
of restrictions ... decompose a 12312 -avoiding
matching into smaller 12312 -avoiding matchings. For notational convenience, we denote
by E
j
the edge (i, j) with i < j.
Lemma 2.1 Let M be a 12312 -avo...
Báo cáo toán học: "The initial involution patterns of permutations" ppsx
... B
T
C
,
where A is of size m ì m, B is of size m ì (n m) and C is of size (n m) ì (n m).
The sizes of blocks are shown on the margins of the matrix.
Let s denote the number of 1’s in B. Then ... elements of π are the last 3 elements of σ, i.e. 5 4 2. The middle part of π is
the electronic journal of combinatorics 14 (2007), #R2 8
9 8 7. The first part of π is the permut...
Báo cáo toán học: "Generalizations of Partial Difference Sets from Cyclotomy to Nonelementary Abelian p-Groups" pdf
... electronic journal of combinatorics 15 (2008), #R125 8
Generalizations of Partial Difference Sets from
Cyclotomy to Nonelementary Abelian p-Groups
John Polhill
Department of Mathematics, Computer ... type partial difference sets [3].
We can create a product of such sets with certain Latin square type partial difference
sets in nonelementary abelian grou...
Báo cáo toán học: "Matchings and Partial Patterns" docx
... 121 and 112 are partial- matching equivalent, while 1213 and 1123
are not equivalent.
4 Partial matchings and fill ings of diagrams
There is a very close relationship between canonical sequences and ... bijection between
-avoiding and τ
′
-avoiding matchings. Since σ and τ are assumed to be partial- matching
equivalent, there is a bijection f between σ-avoiding and τ-avoidi...
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