6533b859fe1ef96bd12b76b8

RESEARCH PRODUCT

Enumeration of Łukasiewicz paths modulo some patterns

Armen PetrossianSergey KirgizovJean-luc Baril

subject

Discrete mathematicsMathematics::CombinatoricsModulo020206 networking & telecommunications0102 computer and information sciences02 engineering and technology[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]01 natural sciencesConstructiveTheoretical Computer ScienceCombinatoricsMathematics::Logic010201 computation theory & mathematics[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]0202 electrical engineering electronic engineering information engineeringEnumerationBijectionMathematics - CombinatoricsDiscrete Mathematics and CombinatoricsComputingMilieux_MISCELLANEOUSMathematics

description

Abstract For any pattern α of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length n ≥ 0 where two paths are equivalent whenever the occurrence positions of α are identical on these paths. As a byproduct, we give a constructive bijection between Motzkin paths and some equivalence classes of Łukasiewicz paths.

yearjournalcountryeditionlanguage
2019-04-01
10.1016/j.disc.2018.12.005https://hal.archives-ouvertes.fr/hal-02414882