Geodesic
On circulant thin Lehman matrices
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 939-959.

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The class of Lehman matrices is a key structure of characterization of minimally non-ideal clutters. The notion of 1-overlapped factorizations of cyclic groups produces an infinite family of circulant thin Lehman matrices. In this paper, we prove essential properties of the 1-overlapped factorizations of cyclic groups and completely determine the shapes of circulant thin Lehman matrices with small constant line sum, which solves the ideal counterpart of the so-called Grinstead's conjecture for the circulant partitionable graphs in this case.
Classification : 05B20, 05C50
Keywords: thin Lehmann matrix, 1-overlapped factorization, cyclic group 
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     title = {On circulant thin {Lehman} matrices},
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Sakuma, Tadashi; Shinohara, Hidehiro. On circulant thin Lehman matrices. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 939-959. http://geodesic.mathdoc.fr/item/JAC_2014__40_4_a8/