Geodesic
Enumeration of unigraphical partitions
Journal of integer sequences, Tome 11 (2008) no. 4.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In the early 1960s, S. L. Hakimi proved necessary and sufficient conditions for a given sequence of positive integers $d_{1}, d_{2}, \dots , d_{n}$ to be the degree sequence of a unique graph (that is, one and only one graph realization exists for such a degree sequence). Our goal in this note is to utilize Hakimi's characterization to prove a closed formula for the function $d_{uni}(2 m)$, the number of "unigraphical partitions" with degree sum $2m$.
Classification : 05A15, 05A17, 05C75, 11P81
Keywords: partition, degree sequence, graph, unigraphical, generating function (Concerned with sequences and ) 
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     title = {Enumeration of unigraphical partitions},
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Hirschhorn, Michael D.; Sellers, James A. Enumeration of unigraphical partitions. Journal of integer sequences, Tome 11 (2008) no. 4. http://geodesic.mathdoc.fr/item/JIS_2008__11_4_a4/