On ( k, n; f )‎-arcs of type (1, n)‎ in PG (2, 9)‎

الملخص EN

In this paper we discussed the existence of (k, n; f) – arcs of type (1, n) in the projective plane of order nine; when Im (f) = {0, 1, } and 1<  < n, where , i.e.

n = 4 or 10.

For this purpose we use the technique in reference [12] and we deduced the example (19, 4; f ) – arc of type (1, 4) when  = 2, and we have an ordinary (13, 4) – arc of type (1, 4) in PG(2, 9), when  = 3.

Also we have the examples (46, 10; f) – arc when  = 2 and the monoidal (11, 10; f) – arc when  = 9, which is of type (1, 10) in PG ( 2, 9 ).

Also we proved there are no (k, 10; f) – arcs of type (1, 10), in PG (2, 9), for other values of  ( ≠ 2 and 9).