Generalized Pascal triangle for binomial coefficients of words

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• 作者：Julien Leroy¹ ; ^{J.Leroy@ulg.ac.be" class="auth_mail" title="E-mail the corresponding author} ; Michel Rigo ; ^{M.Rigo@ulg.ac.be" class="auth_mail" title="E-mail the corresponding author} ; Manon Stipulanti² ; ^{M.Stipulanti@ulg.ac.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 28A80 ; secondary ; 28A78 ; 11B85 ; 68R15
• 刊名：Advances in Applied Mathematics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：80
• 期：Complete
• 页码：24-47
• 全文大小：805 K

文摘

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0,1]×[0,1]$[0,1]\times [0,1]$ associated with this extended Pascal triangle modulo a prime p.