TY - JOUR
T1 - On rational Dyck paths and the enumeration of factor-free Dyck words
AU - Birmajer, Daniel
AU - Gil, Juan B.
AU - Weiner, Michael D.
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/7/31
Y1 - 2018/7/31
N2 - Motivated by independent results of Bizley and Duchon, we study rational Dyck paths and their subset of factor-free elements. On the one hand, we give a bijection between rational Dyck paths and regular Dyck paths with ascents colored by factor-free words. This bijection leads to a new statistic based on the reducibility level of the paths for which we provide a corresponding formula. On the other hand, we prove an inverse relation for certain sequences defined via partial Bell polynomials, and we use it to derive a formula for the enumeration of factor-free words. In addition, we give alternative formulas for various enumerative sequences that appear in the context of rational Dyck paths.
AB - Motivated by independent results of Bizley and Duchon, we study rational Dyck paths and their subset of factor-free elements. On the one hand, we give a bijection between rational Dyck paths and regular Dyck paths with ascents colored by factor-free words. This bijection leads to a new statistic based on the reducibility level of the paths for which we provide a corresponding formula. On the other hand, we prove an inverse relation for certain sequences defined via partial Bell polynomials, and we use it to derive a formula for the enumeration of factor-free words. In addition, we give alternative formulas for various enumerative sequences that appear in the context of rational Dyck paths.
UR - http://www.scopus.com/inward/record.url?scp=85044314948&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044314948&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2018.02.020
DO - 10.1016/j.dam.2018.02.020
M3 - Article
AN - SCOPUS:85044314948
SN - 0166-218X
VL - 244
SP - 36
EP - 43
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -