Exact Recursion Relation for 2 × N Arrays of Dumbbells
- 1 October 1970
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (10) , 3095-3099
- https://doi.org/10.1063/1.1665098
Abstract
It is shown that A(q, N), the number of ways of arranging q indistinguishable dumbbells on a 2 × N rectangular array of compartments, is exactly described by the recursion relationA(q,N)=A(q,N−1)+2A(q−1,N−1)+A(q−1,N−2)−A(q−3,N−3). For large values of N the normalization of the distribution generated by this recursion relation is found to be 0.665(3.214)N and the maximum number of arrangements occurs when the array is approximately 61% occupied.Keywords
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