Some q-congruences for homogeneous and quasi-homogeneous multiple q-harmonic sums
Copyright policy )Some q-congruences for homogeneous and quasi-homogeneous multiple q-harmonic sums
We show some new Wolstenholme type $q$-congruences for some classes of multiple $q$-harmonic sums of arbitrary depth with strings of indices composed of ones, twos and threes. Most of these results are $q$-extensions of the corresponding congruences for ordinary multiple harmonic sums obtained by the authors in a previous paper. Finally, we pose a conjecture concerning two kinds of cyclic sums of multiple $q$-harmonic sums.
This article is based on the previous version, but the results have been reworked and extended substantially
\(q\)-binomial identity, degenerate Bernoulli numbers, Settore MAT/05 - ANALISI MATEMATICA, 11B65, 30E05, 11A07, Binomial coefficients; factorials; \(q\)-identities, duality relations, FOS: Mathematics, Mathematics - Combinatorics, Congruences; primitive roots; residue systems, multiple \(q\)-harmonic sum, Combinatorics (math.CO), \(q\)-congruence
\(q\)-binomial identity, degenerate Bernoulli numbers, Settore MAT/05 - ANALISI MATEMATICA, 11B65, 30E05, 11A07, Binomial coefficients; factorials; \(q\)-identities, duality relations, FOS: Mathematics, Mathematics - Combinatorics, Congruences; primitive roots; residue systems, multiple \(q\)-harmonic sum, Combinatorics (math.CO), \(q\)-congruence
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