کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4595294 | 1335807 | 2008 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Frobenius Problem and dead ends in integers
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
Let a and b be positive and relatively prime integers. We show that the following are equivalent: (i) d is a dead end in the (symmetric) Cayley graph of Z with respect to a and b, (ii) d is a Frobenius value with respect to a and b (it cannot be written as a non-negative or non-positive integer linear combination of a and b), and d is maximal (in the Cayley graph) with respect to this property. In addition, for given integers a and b, we explicitly describe all such elements in Z. Finally, we show that Z has only finitely many dead ends with respect to any finite symmetric generating set. In Appendix A we show that every finitely generated group has a generating set with respect to which dead ends exist.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 128, Issue 5, May 2008, Pages 1211-1223
Journal: Journal of Number Theory - Volume 128, Issue 5, May 2008, Pages 1211-1223