... teaching Chinese as
a foreign language: A case study of native Chinese teachers in Beijing. In Language
alternation, language choice and language encounter in international education, eds.
Hartmut ... words: Chinese as a foreign language; English as a lingua franca; Sinophone identity;
code choice; multilingual classroom
Background
While Chine...
... integrated
framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms
that have been used in Systems Biology including Boolean networks, Bayesian ... used for
modeling dynamical systems in several areas. Systems of non-linear ordinary differential equations (ODEs)
have been used in SB to describe the variation of the amount...
... parity-reversing.
It follows that in the signed sum of walks in W all terms corresponding to walks in N
cancel, leaving only the walks that correspond to permutations of {1, 2, ,n/2} with no
ascending ... correspondence with lattice walks. Interestingly, however, by
providing a combinatorial proof of this correspondence, in section 3 below, we will be giving
an indepe...
... factorisation of Motzkin paths.
2.1 Motzkin Paths with Vertex-visits
Motzkin paths may be factored recursively in terms of shorter Motzkin paths. In particu-
lar, every adsorbing Motzkin path is either ... model of an adsorbing polymer can be defined by letting the path be attracted
to an adsorbing line. In models of Motzkin paths, the adsorbing line will be the...
... σ
θ
∈ θ, and by construction in
both permutations there is an increasing chain starting at position 1, while the remaining
values form a decreasing chain; in σ
θ
, however, the increasing chain is ... domain and codomain in this case, taking order-equivalent
functions corresponds to “wrapping around” independently both in the domain and
in the codomain (not necessarily by the s...
... Otago, New Zealand
mike@cs.otago.ac.nz
M. M. Murphy and N. Ruˇskuc
School of Mathematics and Statistics
University of St Andrews, Scotland, KY16 9SS
nik@mcs.st -and. ac.uk and max@mcs.st -and. ac.uk
Submitted: ... Permutations, Antichains, Atomic Classes and Stack
Sorting”, Ph.D. Thesis, University of St Andrews, St Andrews, Scotland, UK (2002).
[8] N. Ray, J. West: Posets of matric...
... are based on the fact that F
(r)
n
(q, t)andL
(r)
n
(q, t) are, respec-
tively, bivariate generating functions for a pair of statistics on linear and circular r-mino
arrangements.
2Linearr-Mino ... Classifications: 11B39, 05A15
Abstract
We introduce a new statistic on linear and circular r-mino arrangements which
leads to interesting polynomial generalizations of the...
... [22], obtained in the context
of pattern-avoiding ordered matchings.
Let us begin by giving a description of 312-avoiding and 231-avoiding partial transver-
sals. We first introduce some terminology. ... J
ℓ
-avoiding filling. It is clear that this construction can be inverted,
thus giving the required biject io n between I
ℓ
-avoiding and J
ℓ
-avoiding transversal partial
fillings of D.
C...
... map
returns the regular binomial coefficients in the Pascal triangle. We obtain the regular
Pascal pyramid if r = 3. For the cases r ≥ 4 we will refer as generalized Pascal pyramids.
The main purp ... k
1
+ ···+ k
m
= n.
In order to prepare the proof of Theorem 5, let introduce the notation of rays in
generalized Pascal pyramids. As usual, a lattice ray in...
... journal of combinatorics 18 (2011), #P127 15
Subgraph densities in signed graphons and
the local Simonovits–Sidorenko conjecture
L´aszl´o Lov´asz
∗
Institute of Mathematics, Eăotvăos Lorand University
Budapest, ... ode in S has neighbors in at most
two of the H
i
. Let F
i
denote the graph consisting of H
i
, its neigh bors in S, and the edges
between H
i
and...
... other standard notation comes
from [1].
the electronic journal of combinatorics 18 (2011), #P149 2
Long path lemma concerning connectivity
and independence number
Shinya Fujita
∗
Alexander Halperin
†
Colton ... theorem and, following the proofs presented in [4], we prove the
following lemma which is o ur main result.
Lemma 1 Let k ≥ 1 be an integer and let G be a g raph of...