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For the Monomer-Dimer lambda_d(p), the Master Algebraic Conjecture | | Paul Federbush
; | | Date: |
5 Sep 2012 | | Abstract: | The author has recently presented two different expressions for lambda_d(p)
of the monomer-dimer problem involving a power series in p, the first jointly
with Shmuel Friedland. These two expressions are certainly equal, but this has
not yet been proven rigorously. The first is naturally developed from
quantities J_i, cluster expansion kernels. The second from the Mayer (or
Virial) series of a dimer gas, in particular from the b_i coefficients in the
Mayer series. The sets {b_i} and {J_i} can be derived from each other. Given an
arbitrary set of values for either the b_i or the J_i, both expressions may be
given in terms of a formal sum. The master algebraic conjecture is that these
two expressions are equivalent. This is detailed in the special case all J_i
are zero. | | Source: | arXiv, 1209.0987 | | Services: | Forum | Review | PDF | Favorites | |
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