  It is known that for an IP${^\star}$ set $A$ in $\mathbb{N}$ and a sequence
$< x_{n}>_{n=1}^{\infty}$ there exists a sum subsystem $<
y_{n}>_{n=1}^{\infty}$ of $< x_{n}>_{n=1}^{\infty}$ such that
  $FS(< y_n>_{n=1}^\infty)\cup FP(< y_n>_{n=1}^\infty)\subseteq A$. Similar
types of results also have been proved for central* sets where the sequences
have been taken from the class of minimal sequences. In this present work we
will prove some analogues results for C$^{\star}$-sets for a more general class
of sequences.

Combinatorics