Abstract
AbstractA PSCA$$(v, t, \lambda )$$
(
v
,
t
,
λ
)
is a multiset of permutations of the v-element alphabet $$\{0, \dots , v-1\}$$
{
0
,
⋯
,
v
-
1
}
, such that every sequence of t distinct elements of the alphabet appears in the specified order in exactly $$\lambda $$
λ
of the permutations. For $$v \geqslant t \geqslant 2$$
v
⩾
t
⩾
2
, we define g(v, t) to be the smallest positive integer $$\lambda $$
λ
, such that a PSCA$$(v, t, \lambda )$$
(
v
,
t
,
λ
)
exists. We show that $$g(6, 3) = g(7, 3) = g(7, 4) = 2$$
g
(
6
,
3
)
=
g
(
7
,
3
)
=
g
(
7
,
4
)
=
2
and $$g(8, 3) = 3$$
g
(
8
,
3
)
=
3
. Using suitable permutation representations of groups, we make improvements to the upper bounds on g(v, t) for many values of $$v \leqslant 32$$
v
⩽
32
and $$3\leqslant t\leqslant 6$$
3
⩽
t
⩽
6
. We also prove a number of restrictions on the distribution of symbols among the columns of a PSCA.
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics
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