Geodesic
Enumeration of plane partitions with a~restricted number of parts
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 349-357

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We use the quantum statistical approach to estimate the number of restricted plane partitions of an integer $n$ with the number of parts not exceeding some finite $N$. We use the analogy between this number theory problem and the enumeration of microstates of the ideal two-dimensional Bose gas. The numbers of restricted plane partitions calculated with the conjectured expression agree well with the exact values for $n$ from $10$ to $20$.
Keywords: Bose gas, restricted partition.
Mots-clés : plane partition 
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     author = {A. Rovenchak},
     title = {Enumeration of plane partitions with a~restricted number of parts},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {349--357},
     publisher = {mathdoc},
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     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a7/}
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A. Rovenchak. Enumeration of plane partitions with a~restricted number of parts. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 349-357. http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a7/