Séminaire Lotharingien de Combinatoire, B51h (2005), 16 pp.

István Kovács

The Number of Indecomposable Schur Rings over a Cyclic 2-Group

Abstract. Indecomposable Schur rings over a cyclic group Z_n of order n are considered. In the case n=p^m, p an odd prime, the total number of such rings was described in terms of Catalan numbers by Liskovets and Pöschel [Discr. Math. 214 (2000), 173-191]. Here, a closed formula is shown for the total number of indecomposable Schur rings over Z_2^m using Catalan and Schröder numbers. The result is obtained after the initial problem is turned into a lattice path problem.

Received: December 29, 2003. Accepted: July 31, 2005. Final Version: September 7, 2005.

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