{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:05:07Z","timestamp":1787321107936,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2020-03912"],"award-info":[{"award-number":["RGPIN-2020-03912"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1802201"],"award-info":[{"award-number":["DMS-1802201"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1,1]]},"abstract":"<jats:p>In the vector space of symmetric functions, the elements of the basis of elementary symmetric functions are (up to a factor) the chromatic symmetric functions of disjoint unions of cliques. We consider their graph complements, the functions $\\{r_{\\lambda}: \\lambda \\text{ an integer partition}\\}$ defined as chromatic symmetric functions of complete multipartite graphs. This basis was first introduced by Penaguiao [ J. Combin. Theory Ser. A, 175 (2020), 105258]. We provide a combinatorial interpretation for the coefficients of the change-of-basis formula between the $r_{\\lambda}$ and the monomial symmetric functions, and we show that the coefficients of the chromatic and Tutte symmetric functions of a graph $G$ when expanded in the $r$-basis enumerate certain intersections of partitions of $V(G)$.<\/jats:p>","DOI":"10.1137\/20m1380314","type":"journal-article","created":{"date-parts":[[2021,11,8]],"date-time":"2021-11-08T11:28:10Z","timestamp":1636370890000},"page":"2647-2661","source":"Crossref","is-referenced-by-count":0,"title":["A Complete Multipartite Basis for the Chromatic Symmetric Function"],"prefix":"10.1137","volume":"35","author":[{"given":"Logan","family":"Crew","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sophie","family":"Spirkl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,11,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2021.102189"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.37236\/10018"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2016.09.019"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2020.112255"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/18M1216201"},{"key":"atypb6","first-page":"401","volume":"9","author":"Cho S.","year":"2018","journal-title":"J. Comb."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2020.103143"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.37236\/8930"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/17M1144805"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"J. A. Ellis-Monaghan and I. Moffatt, eds.\n                      Handbook of the Tutte Polynomial\n                      , Chapman & Hall\/CRC Press, Boca Raton, FL, 2022.","DOI":"10.1201\/9780429161612"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.37236\/8211"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s00026-019-00426-x"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.90.8.3607"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/7096"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-01-00373-3"},{"key":"atypb16","first-page":"210","volume":"75","author":"Heil S.","year":"2019","journal-title":"Australas. J. Combin."},{"key":"atypb17","first-page":"131","volume":"20","author":"Macdonald I. G.","year":"1988","journal-title":"S\u00e9minaire Lotharingien de Combinatoire"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"I. G. Macdonald,\n                      Symmetric Functions and Hall Polynomials\n                      , Oxford University Press, New York, 1995.","DOI":"10.1093\/oso\/9780198534891.001.0001"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.5802\/aif.1706"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2013.12.006"},{"key":"atypb21","unstructured":"G. Panova,\n                      personal communication\n                      , 2018."},{"key":"atypb22","unstructured":"A. Paunov,\n                      Planar Graphs and Stanley's Chromatic Functions\n                      , preprint,https:\/\/arxiv.org\/abs\/1702.05787, 2017."},{"key":"atypb23","unstructured":"B. Pawlowski,\n                      Chromatic Symmetric Functions via the Group Algebra of ${{S}}_n$\n                      , preprint,https:\/\/arxiv.org\/abs\/1802.05470, 2018."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2020.105258"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1006\/aima.1995.1020"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00146-0"},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"R. P. Stanley and S. Fomin,\n                      Enumerative Combinatorics\n                      , Vol. 2, Cambridge Stud. Adv. Math. 62, Cambridge University Press, Cambridge, 1999.","DOI":"10.1017\/CBO9780511609589"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-018-1928-2"},{"key":"atypb29","unstructured":"D. G. Wang and M. M. Wang,\n                      Non-Schur-positivity of Chromatic Symmetric Functions\n                      , preprint,https:\/\/arxiv.org\/abs\/2001.00181, 2020."},{"key":"atypb30","unstructured":"M. Zabrocki,\n                      A Module for the Delta Conjecture\n                      , preprinthttps:\/\/arxiv.org\/abs\/1902.08966, 2019."}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1380314","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:06:39Z","timestamp":1787317599000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1380314"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,1]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1380314"],"URL":"https:\/\/doi.org\/10.1137\/20m1380314","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,1]]}}}