{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T08:19:15Z","timestamp":1787386755682,"version":"3.56.0"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[1997,11]]},"abstract":"<jats:p>The stacknumber (queuenumber) of a poset is defined as the stacknumber (queuenumber) of its Hasse diagram viewed as a directed acyclic graph. Upper bounds on the queuenumber of a poset are derived in terms of its jumpnumber, its length, its width, and the queuenumber of its covering graph. A lower bound of $\\Omega(\\sqrt n)$ is shown for the queuenumber of the class of n-element planar posets. The queuenumber of a planar poset is shown to be within a small constant factor of its width. The stacknumber of n-element posets with planar covering graphs is shown to be $\\Theta(n)$. These results exhibit sharp differences between the stacknumber and queuenumber of posets as well as between the stacknumber (queuenumber) of a poset and the stacknumber (queuenumber) of its covering graph.<\/jats:p>","DOI":"10.1137\/s0895480193252380","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"599-625","source":"Crossref","is-referenced-by-count":35,"title":["Stack and Queue Layouts of Posets"],"prefix":"10.1137","volume":"10","author":[{"given":"Lenwood S.","family":"Heath","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sriram V.","family":"Pemmaraju","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(79)90021-2"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"G. Birkhoff,\n                      Lattice Theory\n                      , American Mathematical Society, Providence, RI, 1940.","DOI":"10.1090\/coll\/025"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0608002"},{"key":"R4","volume-title":"Introduction to lattices and order","author":"Davey B.","year":"1990"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.2307\/1969503"},{"key":"R6","first-page":"463","volume":"2","author":"Erd\u00f6s P.","year":"1935","journal-title":"Compositio Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-437X","issn-type":"print"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0403042"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0405031"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539795291550"},{"key":"R10","unstructured":"L. S. Heath, S. V. Pemmaraju, and C. J. Ribbens,\n                      Sparse Matrix\u2010Vector Multiplication on a Small Linear Array\n                      , Technical Report TR93\u201011, Dept. of Computer Science, Virginia Polytechnic and State University, Blacksburg, VA, 1993."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"LenwoodHeath, SriramPemmaraju, AnnTrenk, Stack and queue layouts of directed acyclic graphs, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol. 9, Amer. Math. Soc., Providence, RI, 1993, 5\u2013111221797","DOI":"10.1090\/dimacs\/009\/02"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539795291550"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0221055"},{"key":"R14","unstructured":"L. T. Q. Hung,\n                      A Planar Poset which Requires 4 Pages\n                      , Institute of Computer Science, University of Wroc\u0142aw, typescript, 1989."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/BF00563521"},{"key":"R16","unstructured":"S. V. Pemmaraju,\n                      Exploring the Powers of Stacks and Queues via Graph Layouts\n                      , Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1992."},{"key":"R17","doi-asserted-by":"crossref","unstructured":"MaciejSys\u0142o, Bounds to the page number of partially ordered sets, Lecture Notes in Comput. Sci., Vol. 411, Springer, Berlin, 1990, 181\u201319591f:06006","DOI":"10.1007\/3-540-52292-1_13"},{"key":"R18","first-page":"261","volume":"2","author":"Sysl\u0142o Maciej","year":"1978","journal-title":"Fund. Inform. (4)"},{"key":"R19","unstructured":"A. Wigderson,\n                      The complexity of the Hamiltonian circuit problem for maximal planar graphs\n                      , Tech. Report 82\u2010298, Electrical Engineering and Computer Science Department, Princeton University, Princeton, NJ, 1982."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/0603036"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(89)90032-9"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895480193252380","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:18:25Z","timestamp":1787318305000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895480193252380"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,11]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1997,11]]}},"alternative-id":["10.1137\/S0895480193252380"],"URL":"https:\/\/doi.org\/10.1137\/s0895480193252380","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,11]]}}}