{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T22:11:46Z","timestamp":1648505506076},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"In this paper we present an algorithm that generates $k$-noncrossing, $\\sigma$-modular diagrams with uniform probability. A diagram is a labeled graph of degree $\\le 1$ over $n$ vertices drawn in a horizontal line with arcs $(i,j)$ in the upper half-plane. A $k$-crossing in a diagram is a set of $k$ distinct arcs $(i_1, j_1), (i_2, j_2),\\ldots,(i_k, j_k)$ with the property $i_1 < i_2 < \\ldots < i_k < j_1 < j_2 < \\ldots < j_k$. A diagram without any $k$-crossings is called a $k$-noncrossing diagram and a stack of length $\\sigma$ is a maximal sequence $((i,j),(i+1,j-1),\\dots,(i+(\\sigma-1),j-(\\sigma-1)))$. A diagram is $\\sigma$-modular if any arc is contained in a stack of length at least $\\sigma$. Our algorithm generates after $O(n^k)$ preprocessing time, $k$-noncrossing, $\\sigma$-modular diagrams in $O(n)$ time and space complexity.<\/jats:p>","DOI":"10.37236\/447","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:58:37Z","timestamp":1578697117000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Uniform Generation of Modular Diagrams"],"prefix":"10.37236","volume":"17","author":[{"given":"Fenix W.D.","family":"Huang","sequence":"first","affiliation":[]},{"given":"Christian M.","family":"Reidys","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,12,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r175\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r175\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:18:53Z","timestamp":1579285133000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r175"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"http:\/\/dx.doi.org\/10.37236\/447","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":["Computational Theory and Mathematics","Geometry and Topology","Theoretical Computer Science","Applied Mathematics","Discrete Mathematics and Combinatorics"],"published":{"date-parts":[[2010,12,10]]}}}