Solomon’s descent algebra is used to define a family of signed measures MW,x for a finite Coxeter group W and x > 0. The measures corresponding to W of type An arise from the theory of card shuffling. Formulas for these measures are obtained and conjectured in special cases. The eigenvalues of the associated Markov chains are computed. By elementary algebraic group theory, choosing a random sem...

Generalized conjugation is the action of a group on its underlying set given by (g, x) 7→ φ(g)xg, where φ : G → G is some fixed endomorphism. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if φ has a nontrivial kernel or if it is an inner automorphism, and we give a construction that allows a part...

We define a Rohlin property for Z-actions on UHF algebras and show a non-commutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. We consider two classes of UHF algebras. For UHF algebras in one class including the CAR algebra, there is one and only one outer conjugacy class of product type actions and for UHF algebra...

Besides being of independent interest in understanding the structure of (partial) MUB collections and their conjugacy classes, satisfactory answers to these questions will help the following investigations: – the search for lower bounds on the number of MUBs and specifically for efficient constructions; – the search for upper bounds on the number of MUBs even for small non-prime-power dimension...

By algebraic group theory, there is a map from the semisimple conjugacy classes of a nite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. We conjecture that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction of ...

for $q in {7,8,9,11,13,16}$, we consider the primitive actions of $l_2(q)$ and use key-moori method 1 as described in [codes, designs and graphs from the janko groups {$j_1$} and{$j_2$}, {em j. combin. math. combin. comput.}, {bf 40} (2002) 143--159., correction to: ``codes, designs and graphs from the janko groups{$j_1$} and {$j_2$}'' [j. combin. math. combin. comput. {bf 40} (2002) 143--159],...