Báo cáo toán học: "LATIN SQUARES OF ORDER" potx
Báo cáo toán học: "LATIN SQUARES OF ORDER" potx
... independent computations of the number of Latin squares of order 10.
We also give counts of Latin rectangles with up to 10 columns, and estimates of the number of
Latin squares of orders up to 15.
Mathematics ... subgraph of degree one. A one-factorization
of G is a partition of E(G) into one-factors. Clearly, the rows of a Latin rectangle R correspond
to the one-fac...
Báo cáo toán học: "Latin squares with forbidden entries" pdf
... coloring of K
2n,2n
using the colors of the list at each edge.
This paper will present the key lemma in the next section and then proceed to the
proof of Theorem 5. We end with some discussions of ... Chessboard squares. Discrete Math. 141 (1995)
47–59.
the electronic journal of combinat orics 13 (2006), #R47 8
Theorem 6 The list chromatic index of a bipartite graph equals the ma...
Báo cáo toán học: "Evolutionary Families of Sets" potx
... the
members of i
S
[S] account for at least five of the seven nonempty subsets of S. Without losing
generality we may assume that the complement in P(S) − {∅} of i
S
[S] is a subset of one of
the following:
(a) ... single member of S.Ifa
(unique) member of S is of cardinality 1, then its unique element is considered to be a distin-
guished vertex of G. The connectedness of...
Báo cáo toán học: "Two Characterizations of Hypercubes" potx
... vertex of G has degree n i.e. G is regular of degree
n.
Claim 3.The graph G is bipartite.
Proof of C l aim 3. If a prime convex P
i
cuts off an edge of a cycle it must cut off
also another edge of ... journal of combinatorics 18 (2011), #P97 2
Two Characterizations of Hypercubes
Juhani Nieminen, Matti Peltola and Pasi Ruotsalainen
Department of Mathematics, University of Oulu...
Báo cáo toán học: "Perfect factorisations of bipartite graphs and Latin squares without proper subrectangles" pptx
... 1: Subsquares of N
2
squares of order 9.
In particular we note that there are 1589 main classes of N
∞
squares of order 9, yet
only 37 of these contain pan-Hamiltonian squares. In terms of reduced ... N
2
squares of order 4, we conclude that N
2
squares of order 9 cannot have proper subsquares except of order 3. The breakdown of
the 1707 main classes according to...
Báo cáo toán học: "A Generalisation of Transversals for Latin Squares'''' docx
... The set of partial latin squares of order n is denoted by PLS(n), and the
set of latin squares of order n by LS(n). We say that P
1
∈ PLS(n) contains P
2
∈ PLS(n)
if every filled cell of P
2
agrees ... question of which plexes are completable to latin
squares. Following that is a section on the existence of plexes in Cayley tables of groups.
Section 4 looks at plexes in la...
Báo cáo toán hoc:"On biembeddings of Latin squares" pdf
... each of which has a
parallel class in one colour. The proof depends on the construction of a biembedding of
a pair of Latin squares of side p, one of which has p
2
(p − 2)/8 subsquares of side ... biembeddings
of Latin squares where paratopic copies are a llowed, and statements about particular
realizations of Latin squares. For Latin squares A and A
′
with common set...
Báo cáo toán học: " Homoclinic solutions of some second-order nonperiodic discrete systems" pptx
... is just the repetition of the proof of Lemma
3.2, we omit the details of its proof.
With the aid of above preparations, now we will give the proof of Theorem 1.2.
Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so we omit
the details of its proof.
Lemma 3.4 Under the conditions of Theorem 1.2, F(x) satisfies the PS condition.
Proof From the proof of Le...
Báo cáo toán học: "One-Factorizations of Regular Graphs of Order 12" pot
... one-factorization of type 4 + 4 + 4 is only possible for three graphs of order
12: the disjoint union of three copies of C
4
, the disjoint union of three copies of K
4
,and
the union of K
4
and the ... properties of the
classified one-factorizations are also tabulated.
1 Introduction
An r-factor of a graph G is an r-regular spanning subgraph of G.Anr-factorization
of G i...
Báo cáo toán học: "The combinatorics of orbital varieties closures of nilpotent order 2 in sl n" docx
... the tableau. Examine
the content of the box to the right of the removed box and that of the box below of the
removed box. Slide the box containing the smaller of these two numbers to the vacant
position. ... (T
2
n
)
†
.
Acknowledgments. The problem of combinatorial description of inclusion of
orbital variety closures in terms of Young tableaux as well as the idea of the c...
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