Báo cáo toán học: "Perfect codes in Cartesian products of 2-paths and infinite paths" pptx
Báo cáo toán học: "Perfect codes in Cartesian products of 2-paths and infinite paths" pptx
... 05C69,05C70,94B60
Abstract
We introduce and study a common generalization of 1-error binary perfect codes
and perfect single error correcting codes in Lee metric, namely perfect codes on
products of paths of length 2 and ... +1+2n is a
factor of 2
k
,andthereissomep such that 2n + k =2
p
− 1.
the electronic journal of combinatorics 12 (2005), #R65 7
Perfect codes...
Báo cáo toán học: "Improved bounds for the number of forests and acyclic orientations in the square lattice" doc
... is
interesting in itself and has been usefully applied to other families of graphs [8].
We describe the method in Section 3, after a short introduction to the Tutte polyonmial
in Section 2. In ... Chang and R. Shrock, Acyclic orientation numbers for families of graphs, State
Univ. of New York at Stony Brook preprint.
[5] N.J. Calkin and H.S. Wilf, The number of independe...
Báo cáo toán học: "Relating different cycle spaces of the same infinite graph" docx
... connection coincide. Among other things, we will be interested in
compactifications of G, which, for in nite graphs, means adding some additional points
and open sets corresponding to the “ends” of G.
An ... Z
X
of X is contained in
the cycle space Z
Y
of Y . In this work, we show how to extend a basis for Z
X
to a
basis of Z
Y
.
1 Introduction
Bonnington and Richter [1] i...
Báo cáo toán học: "On Computing the Distinguishing Numbers of Trees and Forests" pps
... contradiction since φ
is a distinguishing k-labeling of T
. Thus, φ is
a distinguishing k-labeling of T so D(T ) ≤ D(T
). By the same argument, we can show that
every distinguishing k-labeling of T
can ... trees.
3 Distinguishing labelings of rooted trees
In this section, we give a characterization of the distinguishing labelings of rooted tree T ,and
show how we can de...
Báo cáo toán học: "A note on a problem of Hilliker and Straus" pps
... 2k
+ 1,
and, since the cardinality of T is at most l(|A|− 1) + 1,
f(¯α, p) + 1 = |A| ≥
log p
l log 2k
+ 1,
completing the proof of Theorem 1.
Since l ≤ k as an immediate consequence of Theorem ... A. Schinzel, Addition of sequences in general fields,
Monatshefte f¨ur Mathematik 82 (1976), 261–268.
[2] D. L. Hilliker, E. G. Straus, Uniqueness of linear combinations (mod p), Journal...
Báo cáo toán học: "Elementary Proofs for Convolution Identities of Abel and Hagen–Rothe" pps
... electronic journal of combinatorics 17 (2010), #N24 2
Elementary Proofs for Convolution Identities
of Abel and Hagen–Rothe
Wenchang Chu
∗
Hangzhou Normal University
Institute of Combin atorial Mathematics
Hangzhou ... Chu, Invers i on Tec hniques and Combinatorial Identities: A quick introduction to
hypergeome tric ev aluations, Math. Appl. 283 (1994), 31 –57.
[2] W. Chu, Generating...
Báo cáo toán học: "Perfect dominating sets in the Cartesian products of prime cycles" docx
... structure of a minimum dominating set of C
n
2n+1
, the Cartesian
product of n copies of the cycle of size 2n + 1, where 2n + 1 is a prime.
Keywords: Perfect Lee codes; dominating sets; defining sets.
1 ... one perfect dominating set, a set S ⊆ V (G) is a minimum dominating
set if and only if it is a perfect dominating set. In [2] Chartrand et al. studied the size
of definin...
Báo cáo toán học: "Perfect matchings in -regular graphs" potx
... Perfect matchings in -regular graphs
Noga Alon
∗
School of Mathematics, Institute for Advanced Study,
Princeton, NJ 08540 and Department of Mathematics,
Raymond and Beverly Sackler Faculty of Exact ... side, and is an easy consequence of the Minc
conjecture [6] for permanents, proved by Br´egman [2] (c.f. also [1] for a probabilistic
description of a proof of Schrijver)....
Báo cáo toán học: " Identifying codes with small radius in some infinite regular graphs" pps
... a subset S
R
of R
and an integer α with 0 ≤ α<w;thesetS obtained as the union of the classes of the
elements of S
R
in the tiling induced by the translations of vectors (w,0) and (α, h)isa
periodic ... identifying radius of codes. In: Proceedings of the 7th Nordic
Combinatorial Conference (eds. T. Harju and I. Honkala), Turku, 1999.
[14] I. Honkala, A. Lobstein: On...
Báo cáo toán học: "Perfect Matchings in Claw-free Cubic Graphs" pdf
... 2-fa ctor of H using
many of the specified edges of H so that when transforming this 2-factor of H to that of
G, each of those edges of H has many ways to make 2-factors of G.
2 Structure of 2-edge-connected ... strings of diamonds and replacing each vertex of H with a
triangle. Since D is chosen maximally, u and v are not in diamonds and therefore H has
the edge...