{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T22:57:01Z","timestamp":1743116221749,"version":"3.40.3"},"publisher-location":"Singapore","reference-count":20,"publisher":"Springer Nature Singapore","isbn-type":[{"type":"print","value":"9789819628445"},{"type":"electronic","value":"9789819628452"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-981-96-2845-2_21","type":"book-chapter","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T16:00:31Z","timestamp":1740067231000},"page":"326-345","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Abelian and\u00a0Stochastic Sandpile Models on\u00a0Complete Bipartite Graphs"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2736-4416","authenticated-orcid":false,"given":"Thomas","family":"Selig","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6609-398X","authenticated-orcid":false,"given":"Haoyue","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,21]]},"reference":[{"key":"21_CR1","doi-asserted-by":"publisher","unstructured":"Alofi, A., Dukes, M.: A note on the lacking polynomial of the complete bipartite graph. Disc. Math. 348(2), 8 (2025). ISSN-0012-365X. https:\/\/doi.org\/10.1016\/j.disc.2024.114323","DOI":"10.1016\/j.disc.2024.114323"},{"key":"21_CR2","doi-asserted-by":"publisher","unstructured":"Aval, J.C., D\u2019Adderio, M., Dukes, M., Hicks, A., Le\u00a0Borgne, Y.: Statistics on parallelogram polyominoes and a q, t-analogue of the Narayana numbers. J. Comb. Theory, Ser. A 123(1), 271\u2013286 (2014). https:\/\/doi.org\/10.1016\/j.jcta.2013.09.001","DOI":"10.1016\/j.jcta.2013.09.001"},{"key":"21_CR3","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.aam.2015.09.018","volume":"73","author":"JC Aval","year":"2016","unstructured":"Aval, J.C., d\u2019Adderio, M., Dukes, M., Le Borgne, Y.: Two operators on sandpile configurations, the sandpile model on the complete bipartite graph, and a cyclic lemma. Adv. Appl. Math. 73, 59\u201398 (2016). https:\/\/doi.org\/10.1016\/j.aam.2015.09.018","journal-title":"Adv. Appl. Math."},{"key":"21_CR4","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1103\/PhysRevLett.59.381","volume":"59","author":"P Bak","year":"1987","unstructured":"Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of the 1\/f noise. Phys. Rev. Lett. 59, 381\u2013384 (1987). https:\/\/doi.org\/10.1103\/PhysRevLett.59.381","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"21_CR5","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1103\/PhysRevA.38.364","volume":"38","author":"P Bak","year":"1988","unstructured":"Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality. Phys. Rev. A 38(1), 364\u2013374 (1988). https:\/\/doi.org\/10.1103\/PhysRevA.38.364","journal-title":"Phys. Rev. A"},{"issue":"7","key":"21_CR6","doi-asserted-by":"publisher","first-page":"1913","DOI":"10.1016\/j.jcta.2013.07.004","volume":"120","author":"Y Chan","year":"2013","unstructured":"Chan, Y., Marckert, J.F., Selig, T.: A natural stochastic extension of the sandpile model on a graph. J. Comb. Theory Ser. A 120(7), 1913\u20131928 (2013). https:\/\/doi.org\/10.1016\/j.jcta.2013.07.004","journal-title":"J. Comb. Theory Ser. A"},{"key":"21_CR7","doi-asserted-by":"publisher","unstructured":"Cori, R., Le\u00a0Borgne, Y.: On computation of Baker and Norine\u2019s rank on complete graphs. Electron. J. Comb. 23(1), P1-31, 47pp. (2016). https:\/\/doi.org\/10.37236\/4350","DOI":"10.37236\/4350"},{"issue":"3","key":"21_CR8","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1016\/S0012-365X(02)00338-2","volume":"256","author":"R Cori","year":"2002","unstructured":"Cori, R., Poulalhon, D.: Enumeration of $$(p, q)$$-parking functions. Disc. Math. 256(3), 609\u2013623 (2002). https:\/\/doi.org\/10.1016\/S0012-365X(02)00338-2","journal-title":"Disc. Math."},{"issue":"4","key":"21_CR9","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1006\/eujc.1999.0366","volume":"21","author":"R Cori","year":"2000","unstructured":"Cori, R., Rossin, D.: On the sandpile group of dual graphs. Eur. J. Comb. 21(4), 447\u2013459 (2000). https:\/\/doi.org\/10.1006\/eujc.1999.0366","journal-title":"Eur. J. Comb."},{"key":"21_CR10","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/0304-3975(84)90116-6","volume":"34","author":"MP Delest","year":"1984","unstructured":"Delest, M.P., Viennot, G.: Algebraic languages and polyominoes enumeration. Theor. Comput. Sci. 34, 169\u2013206 (1984). https:\/\/doi.org\/10.1016\/0304-3975(84)90116-6","journal-title":"Theor. Comput. Sci."},{"key":"21_CR11","doi-asserted-by":"publisher","unstructured":"Derycke, H., Dukes, M., Le\u00a0Borgne, Y.: The sandpile model on the complete split graph: $$ q, t $$-schr\u00f6der polynomials, sawtooth polyominoes, and a cyclic lemma. ArXiv preprint (2024). https:\/\/doi.org\/10.48550\/arXiv.2402.15372","DOI":"10.48550\/arXiv.2402.15372"},{"issue":"14","key":"21_CR12","doi-asserted-by":"publisher","first-page":"1613","DOI":"10.1103\/PhysRevLett.64.1613","volume":"64","author":"D Dhar","year":"1990","unstructured":"Dhar, D.: Self-organized critical state of sandpile automaton models. Phys. Rev. Lett. 64(14), 1613\u20131616 (1990). https:\/\/doi.org\/10.1103\/PhysRevLett.64.1613","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"21_CR13","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.physa.2006.04.004","volume":"369","author":"D Dhar","year":"2006","unstructured":"Dhar, D.: Theoretical studies of self-organized criticality. Phys. A Stat. Mech. Appl. 369(1), 29\u201370 (2006). https:\/\/doi.org\/10.1016\/j.physa.2006.04.004","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"21_CR14","doi-asserted-by":"publisher","unstructured":"Dukes, M.: The sandpile model on the complete split graph, Motzkin words, and tiered parking functions. J. Comb. Theory Ser. A 180, 15 (2021). https:\/\/doi.org\/10.1016\/j.jcta.2021.105418. id\/No 105418","DOI":"10.1016\/j.jcta.2021.105418"},{"issue":"4","key":"21_CR15","doi-asserted-by":"publisher","first-page":"816","DOI":"10.1016\/j.jcta.2013.01.004","volume":"120","author":"M Dukes","year":"2013","unstructured":"Dukes, M., Le Borgne, Y.: Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a $$q, t$$-Narayana polynomial. J. Comb. Theory Ser. A 120(4), 816\u2013842 (2013). https:\/\/doi.org\/10.1016\/j.jcta.2013.01.004","journal-title":"J. Comb. Theory Ser. A"},{"key":"21_CR16","doi-asserted-by":"publisher","unstructured":"Dukes, M., Selig, T., Smith, J.P., Steingr\u00edmsson, E.: Permutation graphs and the abelian sandpile model, tiered trees and non-ambiguous binary trees. Electron. J. Comb. 26(3), P3\u201329, 25pp. (2019). https:\/\/doi.org\/10.37236\/8225","DOI":"10.37236\/8225"},{"key":"21_CR17","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.ejc.2019.05.008","volume":"81","author":"M Dukes","year":"2019","unstructured":"Dukes, M., Selig, T., Smith, J.P., Steingr\u00edmsson, E.: The abelian sandpile model on Ferrers graphs - a classification of recurrent configurations. Eur. J. Comb. 81, 221\u2013241 (2019). https:\/\/doi.org\/10.1016\/j.ejc.2019.05.008","journal-title":"Eur. J. Comb."},{"key":"21_CR18","doi-asserted-by":"publisher","unstructured":"Selig, T.: Combinatorial aspects of sandpile models on wheel and fan graphs. Eur. J. Comb. 110, 23 (2023). https:\/\/doi.org\/10.1016\/j.ejc.2022.103663. id\/No 103663","DOI":"10.1016\/j.ejc.2022.103663"},{"key":"21_CR19","doi-asserted-by":"publisher","unstructured":"Selig, T.: The stochastic sandpile model on complete graphs. Electron. J. Comb. 31(3), P3-26, 29pp. (2024). https:\/\/doi.org\/10.37236\/12780","DOI":"10.37236\/12780"},{"key":"21_CR20","doi-asserted-by":"publisher","unstructured":"Selig, T., Smith, J.P., Steingr\u00edmsson, E.: EW-tableaux, Le-tableaux, tree-like tableaux and the abelian sandpile model. Electron. J. Comb. 25(3), P3-14, 32pp. (2018). https:\/\/doi.org\/10.37236\/7480","DOI":"10.37236\/7480"}],"container-title":["Lecture Notes in Computer Science","WALCOM: Algorithms and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-96-2845-2_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T16:00:34Z","timestamp":1740067234000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-96-2845-2_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9789819628445","9789819628452"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-981-96-2845-2_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"21 February 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"WALCOM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference and Workshops on Algorithms and Computation","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Chengdu","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 February 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 March 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"walcom2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/tcsuestc.com\/walcom2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}