Geodesic
The Number of Indecomposable Schur Rings over a Cyclic 2-Group
Séminaire lotharingien de combinatoire, Tome 51 (2004-2005)

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Indecomposable Schur rings over a cyclic group Zn of order n are considered. In the case n=pm, 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 Z2m using Catalan and Schröder numbers. The result is obtained after the initial problem is turned into a lattice path problem. 

@article{SLC_2004-2005_51_a7,
     author = {Istv\'an Kov\'acs},
     title = {The {Number} of {Indecomposable} {Schur} {Rings} over a {Cyclic} {2-Group}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {51},
     year = {2004-2005},
     url = {http://geodesic.mathdoc.fr/item/SLC_2004-2005_51_a7/}
}
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István Kovács. The Number of Indecomposable Schur Rings over a Cyclic 2-Group. Séminaire lotharingien de combinatoire, Tome 51 (2004-2005). http://geodesic.mathdoc.fr/item/SLC_2004-2005_51_a7/