{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:44:24Z","timestamp":1773816264135,"version":"3.50.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,10,16]],"date-time":"2020-10-16T00:00:00Z","timestamp":1602806400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,16]],"date-time":"2020-10-16T00:00:00Z","timestamp":1602806400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC Nos.11431007"],"award-info":[{"award-number":["NSFC Nos.11431007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC Nos.11601172"],"award-info":[{"award-number":["NSFC Nos.11601172"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC Nos.11971195"],"award-info":[{"award-number":["NSFC Nos.11971195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC Nos. 11431007"],"award-info":[{"award-number":["NSFC Nos. 11431007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC Nos. 11601172"],"award-info":[{"award-number":["NSFC Nos. 11601172"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC Nos. 11971195"],"award-info":[{"award-number":["NSFC Nos. 11971195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["no.2662015PY217"],"award-info":[{"award-number":["no.2662015PY217"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s00454-020-00249-1","type":"journal-article","created":{"date-parts":[[2020,10,16]],"date-time":"2020-10-16T17:02:35Z","timestamp":1602867755000},"page":"876-901","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tilings of Convex Polyhedral Cones and Topological Properties of Self-Affine Tiles"],"prefix":"10.1007","volume":"66","author":[{"given":"Ya-min","family":"Yang","sequence":"first","affiliation":[]},{"given":"Yuan","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,16]]},"reference":[{"issue":"2","key":"249_CR1","first-page":"549","volume":"112","author":"Ch Bandt","year":"1991","unstructured":"Bandt, Ch.: Self-similar sets. V. Integer matrices and fractal tilings of $${\\bf R}^n$$. Proc. Amer. Math. Soc. 112(2), 549\u2013562 (1991)","journal-title":"Proc. Am. Math. Soc."},{"key":"249_CR2","first-page":"15","volume":"4","author":"NG de Bruijn","year":"1956","unstructured":"de Bruijn, N.G.: On number systems. Nieuw Arch. Wisk. 4, 15\u201317 (1956)","journal-title":"Nieuw Arch. Wisk."},{"issue":"4","key":"249_CR3","doi-asserted-by":"publisher","first-page":"733","DOI":"10.2307\/2372648","volume":"76","author":"Ch Davis","year":"1954","unstructured":"Davis, Ch.: Theory of positive linear dependence. Amer. J. Math. 76(4), 733\u2013746 (1954)","journal-title":"Am. J. Math."},{"key":"249_CR4","unstructured":"Gerstenhaber, M.: Theory of convex polyhedral cones. Activity Analysis of Production and Allocation. Cowles Commission Monograph, vol. 13, pp. 298\u2013316. Wiley, New York (1951)"},{"issue":"2","key":"249_CR5","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/s00041-001-4007-6","volume":"1","author":"K Gr\u00f6chenig","year":"1994","unstructured":"Gr\u00f6chenig, K., Haas, A.: Self-similar lattice tilings. J. Fourier Anal. Appl. 1(2), 131\u2013170 (1994)","journal-title":"J. Fourier Anal. Appl."},{"key":"249_CR6","volume-title":"Tilings and Patterns","author":"B Gr\u00fcnbaum","year":"1987","unstructured":"Gr\u00fcnbaum, B., Shephard, G.C.: Tilings and Patterns. W.H. Freeman and Company, New York (1987)"},{"issue":"5","key":"249_CR7","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1512\/iumj.1981.30.30055","volume":"30","author":"JE Hutchinson","year":"1981","unstructured":"Hutchinson, J.E.: Fractals and self-similarity. Indiana Univ. Math. J. 30(5), 713\u2013747 (1981)","journal-title":"Indiana Univ. Math. J."},{"key":"249_CR8","doi-asserted-by":"crossref","unstructured":"Kenyon, R.: Self-replicating tilings. In: Symbolic Dynamics and Its Applications (New Haven 1991). Contemp. Math., vol. 135, pp. 239\u2013263. Amer. Math. Soc., Providence (1992)","DOI":"10.1090\/conm\/135\/1185093"},{"key":"249_CR9","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/BF02774038","volume":"97","author":"R Kenyon","year":"1997","unstructured":"Kenyon, R.: Projecting the one-dimensional Sierpinski gasket. Israel J. Math. 97, 221\u2013238 (1997)","journal-title":"Israel J. Math."},{"issue":"1","key":"249_CR10","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1006\/aima.1996.0045","volume":"121","author":"JC Lagarias","year":"1996","unstructured":"Lagarias, J.C., Wang, Y.: Self-affine tiles in $${{\\mathbb{R}}}^n$$. Adv. Math. 121(1), 21\u201349 (1996)","journal-title":"Adv. Math."},{"issue":"1","key":"249_CR11","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1112\/jlms\/54.1.161","volume":"54","author":"JC Lagarias","year":"1996","unstructured":"Lagarias, J.C., Wang, Y.: Integral self-affine tiles in $${\\mathbb{R}}^n$$. I. Standard and nonstandard digit sets. J. London Math. Soc. 54(1), 161\u2013179 (1996)","journal-title":"J. Lond. Math. Soc."},{"issue":"1","key":"249_CR12","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/BF02647948","volume":"3","author":"JC Lagarias","year":"1997","unstructured":"Lagarias, J.C., Wang, Y.: Integral self-affine tiles in $${\\mathbb{R}}^n$$. Part II: Lattice tilings. J. Fourier Anal. Appl. 3(1), 83\u2013102 (1997)","journal-title":"J. Fourier Anal. Appl."},{"key":"249_CR13","doi-asserted-by":"crossref","unstructured":"Lai, Ch.-K., Lau, K.-S., Rao, H.: Spectral structure of digit sets of self-similar tiles on $${\\mathbb{R}}^1$$. Trans. Am. Math. Soc. 365(7), 3831\u20133850 (2013)","DOI":"10.1090\/S0002-9947-2013-05787-X"},{"key":"249_CR14","doi-asserted-by":"crossref","unstructured":"Lai, Ch.-K., Lau, K.-S., Rao, H.: Classification of tile digit sets as product-forms. Trans. Am. Math. Soc. 369(1), 623\u2013644 (2017)","DOI":"10.1090\/tran\/6703"},{"issue":"4","key":"249_CR15","doi-asserted-by":"publisher","first-page":"1401","DOI":"10.1090\/S0002-9947-02-03207-5","volume":"355","author":"K-S Lau","year":"2003","unstructured":"Lau, K.-S., Rao, H.: On one-dimensional self-similar tilings and $$pq$$-tiles. Trans. Amer. Math. Soc. 355(4), 1401\u20131414 (2003)","journal-title":"Trans. Am. Math. Soc."},{"key":"249_CR16","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1215\/S0012-7094-71-03825-7","volume":"38","author":"I Niven","year":"1971","unstructured":"Niven, I.: A characterization of complementing sets of pairs of integers. Duke Math. J. 38, 193\u2013203 (1971)","journal-title":"Duke Math. J."},{"issue":"2","key":"249_CR17","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1112\/plms\/s3-37.2.213","volume":"37","author":"AM Odlyzko","year":"1978","unstructured":"Odlyzko, A.M.: Non-negative digit sets in positional number systems. Proc. London Math. Soc. 37(2), 213\u2013229 (1978)","journal-title":"Proc. Lond. Math. Soc."},{"key":"249_CR18","unstructured":"Rao, H., Yang, Y.-M., Zhang, Y.: Characterization of complementing pairs of $$(\\mathbb{Z}_{\\ge 0})^n$$ (2020). arXiv:2005.09204"},{"key":"249_CR19","series-title":"Princeton Mathematical Series","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis Princeton Mathematical Series, vol. 28. Princeton University Press, Princeton (1970)"},{"key":"249_CR20","doi-asserted-by":"crossref","unstructured":"Vince, A.: Digit tiling of Euclidean space. In: Directions in Mathematical Quasicrystals. CRM Monogr. Ser., vol. 13, pp. 329\u2013370. Amer. Math. Soc., Providence (2000)","DOI":"10.1090\/crmm\/013\/12"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00249-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-020-00249-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00249-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,16]],"date-time":"2021-10-16T01:22:54Z","timestamp":1634347374000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-020-00249-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,16]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["249"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00249-1","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,16]]},"assertion":[{"value":"2 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 June 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 September 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 October 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}