36 citations · 89 across the 20 of their papers we have counts for
5 papers · 1 filter
Cycle up-down permutations
Emeric Deutsch, Sergi Elizalde
A permutation is defined to be cycle-up-down if it is a product of cycles that, when written starting with their smallest element, have an up-down pattern. We prove bijectively and…
On basic forbidden patterns of functions
Sergi Elizalde, Yangyang Liu
The allowed patterns of a map on a one-dimensional interval are those permutations that are realized by the relative order of the elements in its orbits. The set of allowed pattern…
The number of permutations realized by a shift
Sergi Elizalde
A permutation p is realized by the shift on N symbols if there is an infinite word on an N-letter alphabet whose successive left shifts by one position are lexicographically in the…
Improved bounds on the number of numerical semigroups of a given genus
Sergi Elizalde
We improve the previously best known lower and upper bounds on the number n_g of numerical semigroups of genus g. Starting from a known recursive description of the tree T of numer…
The largest and the smallest fixed points of permutations
Emeric Deutsch, Sergi Elizalde
We give a new interpretation of the derangement numbers d_n as the sum of the values of the largest fixed points of all non-derangements of length n-1. We also show that the analog…