6533b835fe1ef96bd129f5d6

RESEARCH PRODUCT

Pattern statistics in faro words and permutations

Jean-luc BarilAlexander BursteinSergey Kirgizov

subject

FOS: Computer and information sciencesMultivariate statisticsDistribution (number theory)Discrete Mathematics (cs.DM)Interlacing0102 computer and information sciences02 engineering and technology[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]01 natural sciencesTheoretical Computer ScienceCombinatoricsStatistics[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]05A05 (Primary) 05A15 05A19 68R15 (Secondary)0202 electrical engineering electronic engineering information engineeringFOS: MathematicsDiscrete Mathematics and CombinatoricsMathematics - CombinatoricsLinear combinationMathematicsDiscrete mathematicsMathematics::Combinatorics020206 networking & telecommunicationsComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Derangement010201 computation theory & mathematicsBijectionCombinatorics (math.CO)AlphabetComputer Science::Formal Languages and Automata TheoryComputer Science - Discrete Mathematics

description

We study the distribution and the popularity of some patterns in $k$-ary faro words, i.e. words over the alphabet $\{1, 2, \ldots, k\}$ obtained by interlacing the letters of two nondecreasing words of lengths differing by at most one. We present a bijection between these words and dispersed Dyck paths (i.e. Motzkin paths with all level steps on the $x$-axis) with a given number of peaks. We show how the bijection maps statistics of consecutive patterns of faro words into linear combinations of other pattern statistics on paths. Then, we deduce enumerative results by providing multivariate generating functions for the distribution and the popularity of patterns of length at most three. Finally, we consider some interesting subclasses of faro words that are permutations, involutions, derangements, or subexcedent words.

yearjournalcountryeditionlanguage
2021-08-01
http://arxiv.org/abs/2010.06270