Combinatorial Nature of the Ground-State Vector of the O(1) Loop Model View Full Text


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Article Info

DATE

2004-03

AUTHORS

A. V. Razumov, Yu. G. Stroganov

ABSTRACT

Studying a possible connection between the ground-state vector for some special spin systems and the so-called alternating-sign matrices, we find numerical evidence that the components of the ground-state vector of the O(1) loop model coincide with the numbers of the states of the so-called fully packed loop model with fixed pairing patterns. The states of the latter system are in one-to-one correspondence with alternating-sign matrices. This allows advancing the hypothesis that the components of the ground-state vector of the O(1) loop model coincide with the cardinalities of the corresponding subsets of the alternating-sign matrices. In a sense, our conjecture generalizes the conjecture of Bosley and Fidkowski, which was refined by Cohn and Propp and proved by Wieland. More... »

PAGES

333-337

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/b:tamp.0000018450.36514.d7

DOI

http://dx.doi.org/10.1023/b:tamp.0000018450.36514.d7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1050154350


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