کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4952530 | 1442037 | 2016 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Maximum number of distinct and nonequivalent nonstandard squares in a word
ترجمه فارسی عنوان
حداکثر تعداد مربع های غیر استاندارد و مجزا در یک کلمه
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کلمات کلیدی
مربع ابلیس، مربعات پارامتریک، مربع نگهداری سفارش
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
چکیده انگلیسی
The combinatorics of nonstandard squares in a word depends on how the equivalence of halves of the square is defined. We consider Abelian squares, parameterized squares, and order-preserving squares. The word uv is an Abelian (parameterized, order-preserving) square if u and v are equivalent in the Abelian (parameterized, order-preserving) sense. The maximum number of ordinary squares in a word is known to be asymptotically linear, but the exact bound is still investigated. We present several results on the maximum number of distinct squares for nonstandard factor equivalence relations. Let SQAbel(n,Ï) and SQAbelâ²(n,Ï) denote the maximum number of Abelian squares in a word of length n over an alphabet of size Ï which are distinct as words and which are nonequivalent in the Abelian sense, respectively. For Ïâ¥2 we prove that SQAbel(n,Ï)=Î(n2), SQAbelâ²(n,Ï)=Ω(n3/2) and SQAbelâ²(n,Ï)=O(n11/6). We also give linear bounds for parameterized and order-preserving squares for alphabets of constant size: SQparam(n,O(1))=Î(n), SQop(n,O(1))=Î(n). The upper bounds have quadratic dependence on the alphabet size for order-preserving squares and exponential dependence for parameterized squares. As a side result we construct infinite words over the smallest alphabet which avoid nontrivial order-preserving squares and nontrivial parameterized cubes (nontrivial parameterized squares cannot be avoided in an infinite word). A preliminary version of this paper was published at DLT 2014 [24]. In this full version we improve or extend the bounds on all three kinds of squares.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Theoretical Computer Science - Volume 648, 4 October 2016, Pages 84-95
Journal: Theoretical Computer Science - Volume 648, 4 October 2016, Pages 84-95
نویسندگان
Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Tomasz WaleÅ,