We report the results of a computer enumeration that found that there are 3155 perfect 1-factorisations (P1Fs) of the complete graph $K_{16}$. Of these, 89 have a nontrivial automorphism group (correcting an earlier claim of 88 by Meszka and Rosa [‘Perfect 1-factorisations of $K_{16}$ with nontrivial automorphism group’, J. Combin. Math. Combin. Comput. 47 (2003), 97–111]). We also (i) describe a new invariant which distinguishes between the P1Fs of $K_{16}$, (ii) observe that the new P1Fs produce no atomic Latin squares of order 15 and (iii) record P1Fs for a number of large orders that exceed prime powers by one.
Blame permeates our social lives. When done properly, blame can facilitate the upholding of moral norms. When done with excessive harshness, however, blame can have significant negative impacts. Here, we develop and validate a scale—the Blame Intensity Inventory—to measure individual differences in the propensity for harsh blame responses. First, we present evidence for its unifactorial structure and test-retest reliability. Then, we present evidence for its convergent and divergent validity by examining relations with existing scales. Finally, across three experiments we show that Blame Intensity uniquely predicts—controlling for other predictors—an important phenomenon: Malicious satisfaction, or gratification upon learning that an offender has been brutally victimized. Results are discussed in terms of important research questions that could be addressed using the Blame Intensity Inventory.
A relation on a k-net(n) (or, equivalently, a set of k − 2 mutually orthogonal Latin squares of order n) is an F2 linear dependence within the incidence matrix of the net. Dukes and Howard ( 2014) showed that any 6-net(10) satisfies at least two non-trivial relations, and classified the relations that could appear in such a net. We find that, up to equivalence, there are 18 526 320 pairs of MOLS satisfying at least one non-trivial relation. None of these pairs extend to a triple. We also rule out one other relation on a set of 3-MOLS from Dukes and Howard's classification.
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