Mathematical Sciences
10.1023/b:tamp.0000018450.36514.d7
doi
2004-03
Combinatorial Nature of the Ground-State Vector of the O(1) Loop Model
2004-03-01
research_article
true
https://scigraph.springernature.com/explorer/license/
http://link.springer.com/10.1023%2FB%3ATAMP.0000018450.36514.d7
333-337
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.
articles
en
2019-04-10T16:41
Pure Mathematics
2305-3135
0040-5779
Theoretical and Mathematical Physics
3
eeeb936e7e97b9efe4a833732b453386c5734106c35b5e4271843cbbfe825e24
readcube_id
Razumov
A. V.
Stroganov
Yu. G.
Springer Nature - SN SciGraph project
pub.1050154350
dimensions_id
138
Institute for High Energy Physics
Institute for High Energy Physics, Protvino, Moscow Oblast, Russia