Counting lattice paths by crossings and major index I: the corner-flipping bijections
نویسندگان
چکیده
We solve two problems regarding the enumeration of lattice paths in \(\mathbb{Z}^2\) with steps \((1,1)\) and \((1,-1)\) respect to major index, defined as sum positions valleys, number certain crossings. The first problem considers crossings a single path fixed horizontal line. second one counts pairs times they cross each other. Our proofs introduce bijections convenient visual descriptions, answers are given by remarkably simple formulas involving \(q\)-binomial coefficients.Mathematics Subject Classifications: 05A19, 05A15, 05A30Keywords: Lattice path, crossing, valley, bijection
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ژورنال
عنوان ژورنال: Combinatorial theory
سال: 2022
ISSN: ['2766-1334']
DOI: https://doi.org/10.5070/c62257880