TY - GEN A1 - Tsarev, Sergey A1 - Wolf, Thomas T1 - Hyperdeterminants as integrable discrete systems N2 - We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A.~Cayley in 1845. We prove integrability (understood as $4d$-consistency) of a nonlinear difference equation defined by the $2 \times 2 \times 2$ - hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the $2\times 2\times 2\times 2$ - hyperdeterminant. T3 - ZIB-Report - 09-17 KW - hyper determinants KW - integrable systems KW - discrete equations KW - large polynomial systems KW - computer algebra KW - Form KW - Reduce KW - Singular Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11292 SN - 1438-0064 ER - TY - JOUR A1 - Wolf, Thomas T1 - Positions in the Game of Go as Complex Systems JF - Proceedings of 2009 IEEE Toronto International Conference (TIC-STH 2009) - Science and Technology for Humanity Y1 - 2009 SN - 978-1-4244-3878-5 ER - TY - JOUR A1 - Tsarev, Sergey A1 - Wolf, Thomas T1 - Hyperdeterminants as integrable discrete systems JF - Journal of Physics A: Mathematical and Theoretical Y1 - 2009 U6 - https://doi.org//10.1088/1751-8113/42/45/454023 VL - 42 ER -