Colloquium ICJ
# (Cyclically) consecutive 123-avoiding permutations

##
by

→
Europe/Paris

Salle Fokko (UCBL-Braconnier)
### Salle Fokko

#### UCBL-Braconnier

21 av Claude Bernard, 69100 VILLEURBANNE

Description

A permutation pi=(pi_1,...,pi_n) is consecutive 123-avoiding if there
is no index i such that pi_i < pi_{i+1} < pi_{i+2}. Similarly, a
permutation pi is cyclically consecutive 123-avoiding if the indices
are viewed modulo n. These two definitions extend to (cyclically)
consecutive S-avoiding permutations, where S is some collection of
permutations on m+1 elements. We determine the asymptotic behavior for
the number of consecutive 123-avoiding permutations by studying an
operator on the space L^2([0,1]^2). In fact, we obtain an asymptotic
expansion for this number. Furthermore we obtain an exact expression
for the number of cyclically consecutive 123-avoiding permutations. A
few results will be stated about the general case of (cyclically)
consecutive S-avoiding permutations. Part of these results are joint
work with Sergey Kitaev and Peter Perry.
The talk will be aimed at a general mathematical audience.