0000000000514994
AUTHOR
Céline Moreira Dos Santos
Right-jumps and pattern avoiding permutations
We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding permutations. We characterize the elements of the basis of this class and we enumerate these "forbidden minimal patterns" by giving their bivariate exponential generating function: we achieve this via a catalytic variable, the number of left-to-right maxima. We show that this generating function is a D-finite function satisfying a nice differential equation of order~2. We give some congruence properties for the coefficients of this generating function, and we sho…
More restrictive Gray code for (1,p)-compositions and relatives
International audience
Some unusual asymptotics for a variant of insertion sort
International audience
Pizza-cutter’s problem and Hamiltonian paths
Summary. The pizza-cutter’s problem is to determine the maximum number of pieces that can be made with n straight cuts through a circular pizza, regardless of the size and shape of the pieces. For ...
Gray code for compositions of n with parts 1 and p
International audience