{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T13:51:31Z","timestamp":1770817891715,"version":"3.50.1"},"publisher-location":"New York, NY, USA","reference-count":29,"publisher":"ACM","license":[{"start":{"date-parts":[[2009,5,31]],"date-time":"2009-05-31T00:00:00Z","timestamp":1243728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2009,5,31]]},"DOI":"10.1145\/1536414.1536511","type":"proceedings-article","created":{"date-parts":[[2009,6,2]],"date-time":"2009-06-02T14:51:13Z","timestamp":1243954273000},"page":"715-724","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":46,"title":["Holant problems and counting CSP"],"prefix":"10.1145","author":[{"given":"Jin-Yi","family":"Cai","sequence":"first","affiliation":[{"name":"University of Wisconsin, Madison, WI, USA"}]},{"given":"Pinyan","family":"Lu","sequence":"additional","affiliation":[{"name":"Microsoft Research Asia, Beijing, China"}]},{"given":"Mingji","family":"Xia","sequence":"additional","affiliation":[{"name":"University of Wisconsin, Madison, WI, USA"}]}],"member":"320","published-online":{"date-parts":[[2009,5,31]]},"reference":[{"key":"e_1_3_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1120582.1120584"},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-70575-8_53"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2006.09.005"},{"key":"e_1_3_2_1_4_1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1007\/b98229","volume-title":"ICALP","author":"Andrei","year":"2004","unstructured":"Andrei A. Bulatov and Martin Grohe. The complexity of partition functions . In ICALP , volume 3142 of Lecture Notes in Computer Science , pages 294 -- 306 . Springer , 2004 . Andrei A. Bulatov and Martin Grohe. The complexity of partition functions. In ICALP, volume 3142 of Lecture Notes in Computer Science, pages 294--306. Springer, 2004."},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.09.011"},{"key":"e_1_3_2_1_6_1","volume-title":"Graph homomorphisms with complex values: A dichotomy theorem. manuscript","author":"Cai Jin-Yi","year":"2009","unstructured":"Jin-Yi Cai , Xi Chen , and Pinyan Lu . Graph homomorphisms with complex values: A dichotomy theorem. manuscript , 2009 . Jin-Yi Cai, Xi Chen, and Pinyan Lu. Graph homomorphisms with complex values: A dichotomy theorem. manuscript, 2009."},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1250790.1250850"},{"key":"e_1_3_2_1_8_1","series-title":"Lecture Notes in Computer Science","first-page":"429","volume-title":"STACS","author":"Cai Jin-Yi","year":"2007","unstructured":"Jin-Yi Cai and Pinyan Lu . On symmetric signatures in holographic algorithms . In STACS , volume 4393 of Lecture Notes in Computer Science , pages 429 -- 440 . Springer , 2007 . Jin-Yi Cai and Pinyan Lu. On symmetric signatures in holographic algorithms. In STACS, volume 4393 of Lecture Notes in Computer Science, pages 429--440. Springer, 2007."},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2008.34"},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.5555\/377810"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(92)90234-7"},{"key":"e_1_3_2_1_12_1","volume-title":"Tensor Geometry. Graduate Texts in Mathematics 130","author":"Dodson C. T. J.","year":"1991","unstructured":"C. T. J. Dodson and T. Poston . Tensor Geometry. Graduate Texts in Mathematics 130 . Springer-Verlag , New York , 1991 . C. T. J. Dodson and T. Poston. Tensor Geometry. Graduate Texts in Mathematics 130. Springer-Verlag, New York, 1991."},{"key":"e_1_3_2_1_13_1","volume-title":"Leslie Ann Goldberg, and Mark Jerrum. The complexity of weighted boolean CSP. CoRR, abs\/0704.3683","author":"Dyer Martin E.","year":"2007","unstructured":"Martin E. Dyer , Leslie Ann Goldberg, and Mark Jerrum. The complexity of weighted boolean CSP. CoRR, abs\/0704.3683 , 2007 . Martin E. Dyer, Leslie Ann Goldberg, and Mark Jerrum. The complexity of weighted boolean CSP. CoRR, abs\/0704.3683, 2007."},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/11786986_5"},{"key":"e_1_3_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1314690.1314691"},{"key":"e_1_3_2_1_16_1","first-page":"246","volume-title":"SODA","author":"Martin","year":"2000","unstructured":"Martin E. Dyer and Catherine S. Greenhill. The complexity of counting graph homomorphisms (extended abstract) . In SODA , pages 246 -- 255 , 2000 . Martin E. Dyer and Catherine S. Greenhill. The complexity of counting graph homomorphisms (extended abstract). In SODA, pages 246--255, 2000."},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20036"},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794266766"},{"key":"e_1_3_2_1_19_1","first-page":"37","article-title":"Reflection positivity, rank connectivity, and homomorphism of graphs","volume":"20","author":"Freedman M.","year":"2007","unstructured":"M. Freedman , L. Lov\u00e1sz , and A. Schrijver . Reflection positivity, rank connectivity, and homomorphism of graphs . J. AMS , 20 : 37 -- 51 , 2007 . M. Freedman, L. Lov\u00e1sz, and A. Schrijver. Reflection positivity, rank connectivity, and homomorphism of graphs. J. AMS, 20:37--51, 2007.","journal-title":"J. AMS"},{"key":"e_1_3_2_1_20_1","volume-title":"A complexity dichotomy for partition functions with mixed signs. CoRR, abs\/0804.1932","author":"Goldberg Leslie Ann","year":"2008","unstructured":"Leslie Ann Goldberg , Martin Grohe , Mark Jerrum , and Marc Thurley . A complexity dichotomy for partition functions with mixed signs. CoRR, abs\/0804.1932 , 2008 . Leslie Ann Goldberg, Martin Grohe, Mark Jerrum, and Marc Thurley. A complexity dichotomy for partition functions with mixed signs. CoRR, abs\/0804.1932, 2008."},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(90)90132-J"},{"key":"e_1_3_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/0031-8914(61)90063-5"},{"key":"e_1_3_2_1_23_1","first-page":"43","volume-title":"Graph Theory and Theoretical Physics","author":"Kasteleyn P. W.","year":"1967","unstructured":"P. W. Kasteleyn . Graph theory and crystal physics . In Graph Theory and Theoretical Physics , pages 43 -- 110 . Academic Press , London , 1967 . P. W. Kasteleyn. Graph theory and crystal physics. In Graph Theory and Theoretical Physics, pages 43--110. Academic Press, London, 1967."},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1080\/14786436108243366"},{"key":"e_1_3_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539797321602"},{"key":"e_1_3_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1137\/0208032"},{"key":"e_1_3_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2004.34"},{"key":"e_1_3_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2006.7"},{"key":"e_1_3_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2007.05.023"}],"event":{"name":"STOC '09: Symposium on Theory of Computing","location":"Bethesda MD USA","acronym":"STOC '09","sponsor":["ACM Association for Computing Machinery","SIGACT ACM Special Interest Group on Algorithms and Computation Theory"]},"container-title":["Proceedings of the forty-first annual ACM symposium on Theory of computing"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1536414.1536511","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1536414.1536511","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:38:51Z","timestamp":1750253931000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1536414.1536511"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,31]]},"references-count":29,"alternative-id":["10.1145\/1536414.1536511","10.1145\/1536414"],"URL":"https:\/\/doi.org\/10.1145\/1536414.1536511","relation":{},"subject":[],"published":{"date-parts":[[2009,5,31]]},"assertion":[{"value":"2009-05-31","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}