Self-converse large sets of pure Mendelsohn triple systems

Lei, Jianguo; Fan, Cui Ling; Zhou, Jun

doi:10.1007/s10114-009-7381-7

Cited by 5 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof When

v \equiv 0, 4 (\mod 12)

, there exists an

{LPMTS}^{*} (v)

by [7, Corollary 2.1], yielding a

0 ‐ normalG (v)

. So we let

v = 12 n + 8

and

n \geq 3

.…”

Section: Doubling Constructionmentioning

confidence: 99%

“…Apply Construction 5.2 by assigning

w (x) = 2

for all points of

⋃_{i = 1}^{s} G_{i}

and

\frac{t}{2}

points of

G_{0}

and then taking

w (x) = 0

for all other points. A

(0^{4}, 1) ‐ POCS (2^{4} : 3)

and a

0^{4} ‐ OF (2^{4})

can be obtained from Lemmas 4.3 and 4.6 in [7], where we replace every block with its three cyclic shifts. A

(2^{4}, 1) ‐ POCS (2^{4} : 3)

and a

2^{4} ‐ OF (2^{4})

exist by [1, Lemma 2.2] and [6, Theorem 3.1], where we replace every block

{x, y, z}

with six blocks in

{{MathClass-open(x, y, z MathClass-close)}^{σ} : σ \in S_{3}}

.…”

Section: Recursive Constructions Via (A B)‐pocssmentioning

confidence: 99%

“…(We call

(x, y, z), (y, z, x), (z, x, y)

three cyclic shifts of

(x, y, z)

.) It is evident that

r ‐ golf

designs can also be regarded as a generalization of the so called self‐converse large set of pure Mendelsohn triple systems of order

v

, shortly denoted by

{LPMTS}^{*} (v)

, which was first introduced in [7]. It is clear that an

{LPMTS}^{*} (v)

implies a

0 ‐ normalG (v)

(for even

v

) or a

1 ‐ normalG (v)

(for odd

v

).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The existence of r‐golf designs

Chang

Zhou

2021

J of Combinatorial Designs

View full text Add to dashboard Cite

An r‐golf design of order v, briefly by r‐G(v), is a large set of idempotent Latin squares of order v (ILS ( v )s) which contains r symmetric ILS ( v )s and v − r − 2 2 transposed pairs of ILS ( v )s. In this paper, we mainly consider the existence problem of r‐G(v)s. We present several recursive constructions and also display some direct constructions. As an application, several infinite classes of r‐G(v)s are determined, including the existence of 0‐G(v)s for more than half of admissible parameters and the existence of r‐G(v)s where v ≡ 110.3em ( mod0.3em 24 ) and r is any admissible integer ( r odd and 1 ≤ r ≤ v − 2).

show abstract

“…Proof When