Let In,k (respectively, Jn,k) be the number of involutions (respectively, fixed-point free involutions) of {1, . . . , n} with k descents. Motivated by Brenti’s conjecture which states that the sequence In,0, In,1, . . . , In,n−1 is log-concave, we prove that the two sequences In,k and J2n,k are unimodal in k, for all n. Furthermore, we conjecture that there are nonnegative integers an,k such t...

Does familiarity promote attraction? Prior research has generally suggested that it does, but a recent set of studies by Norton, Frost, and Ariely (2007) challenged that assumption. Instead, they found that more information about another person, when that information was randomly selected from lists of trait adjectives, using a trait evaluation paradigm, promoted perceptions of dissimilarity an...

Linear codes are widely employed in communication systems, consumer electronics, and storage devices. All linear codes over finite fields can be generated by a generator matrix. Due to this, the generator matrix approach is called a fundamental construction of linear codes. This is the only known construction method that can produce all linear codes over finite fields. Recently, a defining-set ...