Group divisible designs of four groups and block size five with configuration (1; 1; 1; 2)

We present constructions and results about GDDs with four groups and block size five in which each block has Configuration $(1, 1, 1, 2)$, that is, each block has exactly one point from three of the four groups and two points from the fourth group. We provide the necessary conditions of the existence of a GDD$(n, 4, 5; \lambda_1, \lambda_2)$ with Configuration $(1, 1, 1, 2)$, and show that the necessary conditions are sufficient for a GDD$(n, 4, 5; \lambda_1,$ $\lambda_2)$ with Configuration $(1, 1, 1, 2)$ if $n \not \equiv 0 ($mod $6)$, respectively. We also show that a GDD$(n, 4, 5; 2n, 6(n - 1))$ with Configuration $(1, 1, 1, 2)$ exists, and provide constructions for a GDD$(n = 2t, 4, 5; n, 3(n - 1))$ with Configuration $(1, 1, 1, 2)$ where $n \not= 12$, and a GDD$(n = 6t, 4, 5; 4t, 2(6t - 1))$ with Configuration $(1, 1, 1, 2)$ where $n \not= 6$ and $18$, respectively

PARTITIONING THE BLOCKS OF A STEINER TRIPLE SYSTEM INTO PARTIAL PARALLEL CLASSES

Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ≤ [v⁄3], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ≤ v ≤ 43. We also show that whenever 2|b, v ≡ 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ≡ 3 (mod 6), there exists an STS(v) whose blocks can be partitioned into partial parallel classes of size 4

Decomposing the blocks of a Steiner triple system of order 4v-3 into partial parallel classes of size v-1

In this report we present a summary and our new results on finding partial parallel classes of uniform size of Steiner triple systems, STS(v). We show several results for STS(4v - 3), where v = 3 mod 12 and v = 9 mod 12. In Chapter 1 we provide background knowledge and introduce the problem. In Chapter 2 we discuss some important known results to the problem, introduce the needed ingredients, and explain the methodology of the construction. Finally, in Chapter 3, we conclude with a summary and discuss possibilities for future work

Hamilton-Waterloo problem with triangle and C9 factors

The Hamilton-Waterloo problem and its spouse-avoiding variant for uniform cycle sizes asks if Kv, where v is odd (or Kv - F, if v is even), can be decomposed into 2-factors in which each factor is made either entirely of m-cycles or entirely of n-cycles. This thesis examines the case in which r of the factors are made up of cycles of length 3 and s of the factors are made up of cycles of length 9, for any r and s. We also discuss a constructive solution to the general (m,n) case which fixes r and s

Results of non-financial corporations in 2012 Q1

Artículo de revist

Results of non-financial corporations in 2011 and the first three quarters of 2012

Artículo de revist

Theta Graph Designs

We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges