The Eulerian distribution on the involutions of the hyperoctahedral group is unimodal

The Eulerian distribution on the involutions of the symmetric group is unimodal, as shown by Guo and Zeng. In this paper we prove that the Eulerian distribution on the involutions of the hyperoctahedral group, when viewed as a colored permutation group, is unimodal in a similar way and we compute its generating function, using signed quasisymmetric functions.Comment: 11 pages, zero figure

Fluctuations of the Shannon capacity in a Raleigh model of wireless communication

Using the fact that the Shannon capacity C of a Raleigh model of wireless channels is a linear statistic of the channel matrix, we calculate its variance var[C]. We find that the expected value of the Shannon capacity is typical in the model considered, that is the coefficient of variation (var[C])^(1/2)/ is small.Comment: 3 pages, 2 figure