139 research outputs found
A construction for variable dimension strong non-overlapping matrices
We propose a method for the construction of sets of variable dimension strong
non-overlapping matrices basing on any strong non-overlapping set of strings
Strings from linear recurrences and permutations: a Gray code
Each positive increasing integer sequence can serve as a
numeration system to represent each non-negative integer by means of suitable
coefficient strings. We analyse the case of -generalized Fibonacci sequences
leading to the binary strings avoiding . We prove a bijection between the
set % of strings of length and the set of permutations of
. Finally, basing on a known Gray code for
those strings, we define a Gray code for ,
where two consecutive permutations differ by an adjacent transposition
Restricting Dyck Paths and 312-avoiding Permutations
Dyck paths having height at most and without valleys at height are
combinatorially interpreted by means of 312-avoding permutations with some
restrictions on their \emph{left-to-right maxima}. The results are obtained by
analyzing a restriction of a well-known bijection between the sets of Dyck
paths and 312-avoding permutations. We also provide a recursive formula
enumerating these two structures using ECO method and the theory of production
matrices. As a further result we obtain a family of combinatorial identities
involving Catalan numbers
- …