Ontology type: schema:ScholarlyArticle Open Access: True
2020-02-04
AUTHORSMinjia Shi, Li Xu, Denis S. Krotov
ABSTRACTIn a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order v, where v=3k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v=3^k$$\end{document}, and 3-rank v-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v-k$$\end{document}. We develop an approach to generalize this bound and estimate the number of isomorphism classes of resolvable STS (v) of 3-rank v-k-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v-k-1$$\end{document} for an arbitrary v of form 3kT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3^kT$$\end{document}, where T is congruent to 1 or 3 modulo 6. More... »
PAGES1037-1046
http://scigraph.springernature.com/pub.10.1007/s10623-020-00725-y
DOIhttp://dx.doi.org/10.1007/s10623-020-00725-y
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