Geodesic
\((-1)\)-enumeration of self-complementary plane partitions
The electronic journal of combinatorics, Tome 12 (2005)

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We prove a product formula for the remaining cases of the weighted enumeration of self–complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removing the other half of the orbit changes the sign of the weight. We use nonintersecting lattice path families to express this enumeration as a Pfaffian which can be expressed in terms of the known ordinary enumeration of self–complementary plane partitions.
DOI : 10.37236/1904
Classification : 05A15, 05A17, 05B45, 11P81, 52C20
Mots-clés : lattice paths, Pfaffian 
Theresia Eisenkölbl. \((-1)\)-enumeration of self-complementary plane partitions. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1904
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     author = {Theresia Eisenk\"olbl},
     title = {\((-1)\)-enumeration of self-complementary plane partitions},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1904},
     zbl = {1063.05008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1904/}
}
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