A class of natural linear characters for the centralizers of elements in the symmetric group is introduced. The character values of the corresponding monomial characters are calculated. They have a surprising combinatorial interpretation.

We classify partitions which are of maximal p-weight for all odd primes p. As a consequence, we show that any non-linear irreducible character of the symmetric and alternating groups vanishes on some element of prime order.

We study the finite groups with an irreducible character χ satisfying the following hypothesis: χ2 has exactly two distinct irreducible constituents, and one of which is linear, and then obtain a result analogous to the Zhmud’s ([8]).

‎let $v$ be an $n$-dimensional complex inner product space‎. ‎suppose‎ ‎$h$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎hrightarrow mathbb{c} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎denote by $v_{chi}(h)$ the symmetry class‎ ‎of tensors associated with $h$ and $chi$‎. ‎let $k(t)in‎ (v_{chi}(h))$ be the operator induced by $tin‎ ‎text{end}(v)$‎. ‎the...

Chinese word segmentation is always much accounted of in ICT-NLP. In this bakeoff, two different systems in ICTNLP participated. The one is SYSTEM_#1 evaluated in three tracks -PK-close, MSR-close and MSR-open, and SYSTEM_#2 PK-open. Through this bakeoff , the development of Chinese segmentation is learned and the problems are found in our systems. 1 System Description Two different systems in ...