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- W2754624893 abstract "Given a real number $lambda > 1$, we say that $d|n$ is a $lambda$-middle divisor of $n$ if $$ sqrt{frac{n}{lambda}} < d leq sqrt{lambda n}. $$ We will prove that there are integers having an arbitrarily large number of $lambda$-middle divisors. Consider the word $$ langle! langle n rangle! rangle_{lambda} := w_1 w_2 ... w_k in {a,b}^{ast}, $$ given by $$ w_i := left{ begin{array}{c l} a & textrm{if } u_i in D_n backslash left(lambda D_nright), b & textrm{if } u_i in left(lambda D_nright)backslash D_n, end{array} right. $$ where $D_n$ is the set of divisors of $n$, $lambda D_n := {lambda d: quad d in D_n}$ and $u_1, u_2, ..., u_k$ are the elements of the symmetric difference $D_n triangle lambda D_n$ written in increasing order. We will prove that the language $$ mathcal{L}_{lambda} := left{langle! langle n rangle! rangle_{lambda} : quad n in mathbb{Z}_{geq 1} right} $$ contains Dyck words having an arbitrarily large number of centered tunnels. We will show a connection between both results." @default.
- W2754624893 created "2017-09-25" @default.
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- W2754624893 date "2017-09-13" @default.
- W2754624893 modified "2023-09-27" @default.
- W2754624893 title "Middle divisors and $sigma$-palindromic Dyck words" @default.
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