What does frobenius number mean?
Definitions for frobenius number
frobe·nius num·ber
This dictionary definitions page includes all the possible meanings, example usage and translations of the word frobenius number.
Wiktionary
Frobenius numbernoun
For a given set of coprime positive integers, the greatest integer that cannot be expressed as a linear combination (with nonnegative integer coefficients) of its elements.
Etymology: After Ferdinand Georg Frobenius.Category:English eponyms
Wikipedia
frobenius number
The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations, for example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number of the set. The Frobenius number exists as long as the set of coin denominations has no common divisor greater than 1. There is an explicit formula for the Frobenius number when there are only two different coin denominations, x {\displaystyle x} and y {\displaystyle y} : the Frobenius number is then x y − x − y {\displaystyle xy-x-y} . If the number of coin denominations is three or more, no explicit formula is known. However, for any fixed number of coin denominations, there is an algorithm computing the Frobenius number in polynomial time (in the logarithms of the coin denominations forming an input). No known algorithm is polynomial time in the number of coin denominations, and the general problem, where the number of coin denominations may be as large as desired, is NP-hard.
Numerology
Chaldean Numerology
The numerical value of frobenius number in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of frobenius number in Pythagorean Numerology is: 2
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"frobenius number." Definitions.net. STANDS4 LLC, 2024. Web. 28 Apr. 2024. <https://www.definitions.net/definition/frobenius+number>.
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