Section: Highlights of the Year

Highlights of the Year

Classical properties of functions such as associativity, although algebraically easy to read, are hard to meaningfully interpret. In [60] Miguel Couceiro and colleagues at the University of Luxembourg (Jean-Luc Marichal, Jimmy Devillet) showed that associative and quasi-trivial operations that are non-decreasing are characterized in terms of total and weak orderings through the so-called single-peakedness property introduced in social choice theory by Duncan Black. This enabled visual interpretations of the above mentioned algebraic properties, and the enumeration of such operations led to several, previously unknown, integer sequences in Sloane’s On-Line Encyclopedia of Integer Sequences (http://www.oeis.org), e.g., A292932 , A292933 , and A292934 .