{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T17:13:07Z","timestamp":1719853987920},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"The Fibonacci word $W$ on an infinite alphabet was introduced in [Zhang et al., Electronic J. Combinatorics 2017 24(2), 2-52] as a fixed point of the morphism $2i\\rightarrow (2i)(2i+1)$, $(2i+1) \\rightarrow (2i+2)$, $i\\geq 0$.
\nHere, for any integer $k>2$, we define the infinite $k$-bonacci word $W^{(k)}$ on the infinite alphabet as $\\varphi_k^{\\omega}(0)$, where the morphism $\\varphi_k$ on the alphabet $\\mathbb{N}$ is defined for any $i\\geq 0$ and any $0\\leq j\\leq k-1$, by
\n\\begin{equation*}
\n\\varphi_k(ki+j) = \\left\\{
\n\\begin{array}{ll}
\n(ki)(ki+j+1) & \\text{if } j = 0,\\cdots ,k-2,\\\\
\n(ki+j+1)& \\text{otherwise}.
\n\\end{array} \\right.
\n\\end{equation*}
\nWe consider the sequence of finite words $(W^{(k)}_n)_{n\\geq 0}$, where\u00a0 $W^{(k)}_n$ is the prefix of $W^{(k)}$ whose length is the $(n+k)$-th $k$-bonacci number. We then provide a recursive formula for the number of palindromes that occur in different positions of $W^{(k)}_n$. Finally, we obtain the structure of all palindromes occurring in $W^{(k)}$ and based on this, we compute the palindrome complexity of $W^{(k)}$, for any $k>2$.<\/jats:p>","DOI":"10.37236\/9406","type":"journal-article","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:41:07Z","timestamp":1600422067000},"source":"Crossref","is-referenced-by-count":3,"title":["Some Properties of the $k$-bonacci Words on Infinite Alphabet"],"prefix":"10.37236","volume":"27","author":[{"given":"Narges","family":"Ghareghani","sequence":"first","affiliation":[]},{"given":"Morteza","family":"Mohammad-Noori","sequence":"additional","affiliation":[]},{"given":"Pouyeh","family":"Sharifani","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,9,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p59\/8178","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p59\/8178","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:41:07Z","timestamp":1600422067000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,10]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"http:\/\/dx.doi.org\/10.37236\/9406","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,10]]}}}