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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*_{2m}
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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