Liu, Bolian \(k\)-common consequents in Boolean matrices. (English) Zbl 0879.04001 Czech. Math. J. 46, No. 3, 523-536 (1996). Let \(Q\) be a binary relation on an \(n\)-element set \(\{a_1,\dots ,a_n\}\) and \(M(Q)\) be its incidence matrix \((m_{ij})\), i.e. \(m_{ij}=1\) if \((a_i,a_j)\in Q\) and \(m_{ij}=0\) otherwise. A subset \(\{a_{i_1},\dots , a_{i_r}\}\) has a common consequent if the rows of \(M(Q)\) corresponding to \(a_{i_1},\dots ,a_{i_r}\) have a 1 in the same \(k\)-th column. The least such \(k\) is denoted by \(L_Q(a_{i_1},\dots ,a_{i_r})\). We denote by \(L_Q(r)\) the maximum of \(L_Q(a_{i_1},\dots ,a_{i_r})\), where the elements run through all groups of cardinality \(r\) for which a common consequent exists. The values of \(L_Q(r)\) are estimated in the paper. The case \(L_Q(2)\) was solved previously by Š. Schwarz. Reviewer: I.Chajda (Olomouc) Cited in 2 Documents MSC: 03E20 Other classical set theory (including functions, relations, and set algebra) 05C30 Enumeration in graph theory Keywords:binary relation; incidence matrix; common consequents × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Š. Schwarz: Common consequents in directed graphs. Czechoslovak Math. J. 35 (1985), no. 110, 212-246. · Zbl 0575.05041 [2] R.A. Brualdi and Bolian Liu: Generalized exponents of primitive directed graphs. J. Graph Theory 14 (1990), no. 4, 483-499. · Zbl 0714.05028 · doi:10.1002/jgt.3190140413 [3] Š. Schwarz: A combinatorial problem arising in finite Markov chains. Math. Slovaca 36 (1986), 21-28. · Zbl 0615.15006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.