Geodesic
Lattice Partitions with a Straight Line
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 287-294

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DOI

In [1], the solution of a problem of distinct digital filter enumeration was expressed in terms of enumerating partitions of a rectangular set of lattice points with a straight line, under certain restrictions. Here, firstly, an explicit expression is derived for the number of such partitions in that and a more general case. Secondly, the asymptotic ratio of partitions to square of lattice dimensions is derived for a square lattice.
DOI : 10.4153/CMB-1986-044-3
Mots-clés : 05A17, 10A45 
Brownrigg, D. R. K. Lattice Partitions with a Straight Line. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 287-294. doi: 10.4153/CMB-1986-044-3
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     title = {Lattice {Partitions} with a {Straight} {Line}},
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     year = {1986},
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     number = {3},
     doi = {10.4153/CMB-1986-044-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-044-3/}
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