Geodesic
Orbits of Pairs in Abelian Groups
Séminaire lotharingien de combinatoire, Tome 70 (2013-2014)

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We compute the number of orbits of pairs in a finitely generated torsion module (more generally, a module of bounded order) over a discrete valuation ring. The answer is found to be a polynomial in the cardinality of the residue field whose coefficients are integers which depend only on the elementary divisors of the module, and not on the ring in question. The coefficients of these polynomials are conjectured to be non-negative integers. 

@article{SLC_2013-2014_70_a7,
     author = {C. P. Anilkumar and Amritanshu Prasad},
     title = {Orbits of {Pairs} in {Abelian} {Groups}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {70},
     year = {2013-2014},
     url = {http://geodesic.mathdoc.fr/item/SLC_2013-2014_70_a7/}
}
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C. P. Anilkumar; Amritanshu Prasad. Orbits of Pairs in Abelian Groups. Séminaire lotharingien de combinatoire, Tome 70 (2013-2014). http://geodesic.mathdoc.fr/item/SLC_2013-2014_70_a7/