{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T09:02:52Z","timestamp":1649149372892},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p> The class of fully semimonotone matrices is well known in the study of the linear complementarity problem. Stone [(1981) Ph.D. thesis, Dept. of Operations Research, Stanford University, Stanford, CA] introduced this class and conjectured that the principal minors of any fully semimonotone Q<jats:sub>0<\/jats:sub>-matrix are non-negative. While the problem is still open, Murthy and Parthasarathy [(1998) Math. Program.82, 401\u2013411] introduced the concept of incidence using which they proved that the principal minors of any matrix in the class of fully copositive Q<jats:sub>0<\/jats:sub>-matrices, a subclass of fully semimonotone Q<jats:sub>0<\/jats:sub>-matrices, are non-negative. In this paper, we study some properties of fully semimonotone matrices in connection with incidence. The main result of the paper shows that Stone's conjecture is true in the special case where the complementary cones have no partial incidence. We also present an interesting characterization of Q<jats:sub>0<\/jats:sub> for matrices with a special structure. This result is very useful in checking whether a given matrix belongs to Q<jats:sub>0<\/jats:sub> provided it has the special structure. Several examples are discussed in connection with incidence and Q<jats:sub>0<\/jats:sub> property. <\/jats:p>","DOI":"10.1142\/s0219198913400367","type":"journal-article","created":{"date-parts":[[2013,7,2]],"date-time":"2013-07-02T08:08:03Z","timestamp":1372752483000},"page":"1340036","source":"Crossref","is-referenced-by-count":2,"title":["ON FULLY SEMIMONOTONE MATRICES"],"prefix":"10.1142","volume":"15","author":[{"given":"G. S. R.","family":"MURTHY","sequence":"first","affiliation":[{"name":"Statistical Quality Control and Operations Research, Indian Statistical Institute, Street No. 8, Habsiguda, Hyderabad 500007, Andhra Pradesh, India"}]},{"given":"T.","family":"PARTHASARATHY","sequence":"additional","affiliation":[{"name":"Indian Statistical Institute, 37\/110, Nelson Manicham Road, Chennai 600029, Tamil Nadu, India"}]},{"given":"R.","family":"SRIDHAR","sequence":"additional","affiliation":[{"name":"Information Analytics, PD &amp; GT, Caterpillar Inc, Peoria IL 61629, USA"}]}],"member":"219","published-online":{"date-parts":[[2013,11,18]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02591696"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2640-4_13"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)00362-9"},{"key":"rf4","unstructured":"R. W.\u00a0Cottle and G. B.\u00a0Dantzig, Mathematics of the Decision Sciences, eds. G. 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