{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:19:59Z","timestamp":1777645199228,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T00:00:00Z","timestamp":1427846400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2015,4]]},"abstract":"<jats:p>\n                    We construct a horizontal mesh algorithm for a study of a special type of mesh root systems of connected positive loop-free edge-bipartite graphs \u0394, with n \u2265 2 vertices, in the sense of [SIAM J. Discrete Math. 27 (2013), 827\u2013854] and [Fund. Inform. 124 (2013), 309-338]. Given such a loop-free edge-bipartite graph \u0394, with the non-symmetric Gram matrix $\\Gcaron_ \\Delta \\isin \\mathbb{M}_n(\\mathbb{Z})$ and the Coxeter transformation $\\Phi_A : \\mathbb{Z}^n \\rarr \\mathbb{Z}^n$ defined by a quasi-triangular matrix morsification $A \\isin \\mathbb{M}_n(\\mathbb{Z})$ of \u0394 satisfying a non-cycle condition, our combinatorial algorithm constructs a \u03a6\n                    <jats:sub>A<\/jats:sub>\n                    -mesh root system structure $\\Gamma(\\Rscr_\\Delta, \\Phi_A)$ on the finite set of all \u03a6\n                    <jats:sub>A<\/jats:sub>\n                    -orbits of the irreducible root system $\\Rscr_\\Delta := {v \\isin \\mathbb{Z}^n; v \\cdot \\Gcaron_\\Delta \\cdot v^{tr} = 1}$ . We apply the algorithm to a graphical construction of a \u03a6\n                    <jats:sub>I<\/jats:sub>\n                    - mesh root system structure $\\Gamma(\\Rscr_I, \\Phi_I)$ on the finite set of \u03a6\n                    <jats:sub>I<\/jats:sub>\n                    -orbits of roots of any poset I with positive definite Tits quadratic form $\\qIcirc : \\mathbb{Z}_I \\rarr \\mathbb{Z}$ .\n                  <\/jats:p>","DOI":"10.3233\/fi-2015-1162","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T01:26:08Z","timestamp":1575336368000},"page":"345-379","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["A Horizontal Mesh Algorithm for a Class of Edge-bipartite Graphs and their Matrix Morsifications"],"prefix":"10.1177","volume":"136","author":[{"given":"Mariusz","family":"Kaniecki","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12\/18, 87-100 Toru\u0144, Poland. kanies@mat.umk.pl; justus@mat.umk.pl; pmalicki@mat.umk.pl; lielow@mat.umk.pl"}]},{"given":"Justyna","family":"Kosakowska","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12\/18, 87-100 Toru\u0144, Poland. kanies@mat.umk.pl; justus@mat.umk.pl; pmalicki@mat.umk.pl; lielow@mat.umk.pl"}]},{"given":"Piotr","family":"Malicki","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12\/18, 87-100 Toru\u0144, Poland. kanies@mat.umk.pl; justus@mat.umk.pl; pmalicki@mat.umk.pl; lielow@mat.umk.pl"}]},{"given":"Grzegorz","family":"Marczak","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12\/18, 87-100 Toru\u0144, Poland. kanies@mat.umk.pl; justus@mat.umk.pl; pmalicki@mat.umk.pl; lielow@mat.umk.pl"}]}],"member":"179","published-online":{"date-parts":[[2015,4,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1162","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1162","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:37Z","timestamp":1777444297000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2015-1162"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["10.3233\/FI-2015-1162"],"URL":"https:\/\/doi.org\/10.3233\/fi-2015-1162","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4]]}}}