A Generalization of the Climbing Stairs Problem II

Azarian, Mohammad K.

doi:10.35834/2004/1601012

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“…The arrangement of the plane partitions of four in Figure 2 or Figure 3 is not random. According to M. K. Azarian [5] (Theorem 1.1), p(n) can be interpreted as the number of different ways to run up a staircase with n steps, taking steps of possibly different sizes, where the order is not important and there is no restriction on the number or the size of each step taken. Any partition λ = (λ 1 , λ 2 , .…”

Section: Introductionmentioning

confidence: 99%

Plane Partitions as Sums over Partitions

Merca,

Radu

2023

Symmetry

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In this paper, we consider complete homogeneous symmetric functions and provide a new formula for the number of plane partitions of n. This formula expresses the number of plane partitions of n in terms of binomial coefficients as a sum over all the partitions of n, considering the multiplicity of the parts greater than one. We obtain similar results for the number of strict plane partition of n and the number of symmetric plane partitions of n.

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Section: Introductionmentioning

confidence: 99%