Martin Klazar
If is a closed set of finite permutations (i.e., a lower ideal in
where
is the set of all finite permutations
and
is the standard containment ordering) and
denotes the set of all
-permutations in
, then the counting function
is subject to various dichotomies and restrictions
forbidding many functions to have this form; this was shown (Electronic
J. of Combinatorics, 2003) by T. Kaiser and M. Klazar. For example, either
for all
or
is eventually constant,
or--another dichotomy--either
for all
with a
constant
or
for all
, where
are the Fibonacci numbers.
In my talk I will present generalizations and extensions of these results to other classes of objects (like those mentioned in the title) and other containments, and I will discuss a general approach to obtain them uniformly as instances of a general metaresult.