Geodesic
On a Class of Combinatorial Diophantine Equations
Séminaire lotharingien de combinatoire, Tome 44 (2000-2001)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We give a combinatorial proof for a second order recurrence for the polynomials pn(x), where pn(k) counts the number of integer-coordinate lattice points x = (x1,...,xn) with ||x|| = \sum_{i=1}^n |xi| = k. This is the main step to get finiteness results on the number of solutions of the diophantine equation pn(x) = pm(y) if n and m have different parity. The combinatorial approach also allows to extend the original diophantine result to more general combinatorial situations. 

@article{SLC_2000-2001_44_a7,
     author = {Peter Kirschenhofer and Oliver Pfeiffer},
     title = {On a {Class} of {Combinatorial} {Diophantine} {Equations}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {44},
     year = {2000-2001},
     url = {http://geodesic.mathdoc.fr/item/SLC_2000-2001_44_a7/}
}
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Peter Kirschenhofer; Oliver Pfeiffer. On a Class of Combinatorial Diophantine Equations. Séminaire lotharingien de combinatoire, Tome 44 (2000-2001). http://geodesic.mathdoc.fr/item/SLC_2000-2001_44_a7/