factorial number造句

• This function has the property that it sublogarithmically at the factorial numbers.
• General properties of mixed radix number systems also apply to the factorial number system.
• The factorial number system is sometimes defined with the 0 ! place omitted because it is always zero.
• The rightmost column shows the digit sums of the factorial numbers ( in the tables default order ).
• The factorial number system uses a varying radix, giving factorials as place values; they are related to Chinese remainder theorem and residue number system enumerations.
• In fact the factorial number system itself is not truly a numeral system in the sense of providing a representation for all natural numbers using only a finite alphabet of symbols.
• The Fibonorial numbers are used in the definition of Fibonomial coefficients ( or Fibonacci-binomial coefficients ) similarly as the factorial numbers are used in the definition of binomial coefficients.
• The sum of the numbers in the factorial number system representation gives the number of inversions of the permutation, and the parity of that sum gives the signature of the permutation.
• This article uses the term " inversion vector " ( v ) like factorial number the left inversion count gives the permutations reverse colexicographic, and the right inversion count gives the lexicographic index.
• In this article, a factorial number representation will be flagged by a subscript " ! ", so for instance 341010 ! stands for 3 6 4 5 1 4 0 3 1 2 0 1, whose value is
• Factorial numbers, considered as discrete objects, are an important concept in classical number theory because they contain many prime factors, but Riemann found a use for their continuous extension that arguably turned out to be even more important.
• In a mixed-radix system such as the factorial number system, the weights form a sequence where each weight is an integral multiple of the previous one, and the number of permitted digit values varies accordingly from position to position.
• But if exact values for large factorials are desired, then special software is required, as in the pseudocode that follows, which implements the classic algorithm to calculate 1, 1?, 1??, 1???, etc . the successive factorial numbers.
• An obvious way to generate permutations of " n " is to generate values for the Lehmer code ( possibly using the factorial number system representation of integers up to " n " ! ), and convert those into the corresponding permutations.
• Sorting by a column that has the omissible 0 on the right makes the factorial numbers in that column correspond to the index numbers in the immovable column on the left . The small columns are reflections of the columns next to them, and can be used to bring those in colexicographic order.
• Unlike single radix systems whose place values are " base " n for both positive and negative integral n, the factorial number base cannot be extended to negative place values as these would be (  " 1 ) !, (  " 2 ) ! and so on, and these values are undefined . ( see factorial)
• Unlike the factorial number system, the combinatorial number system of degree " k " is not a mixed radix system : the part \ tbinom { c _ i } i of the number " N " represented by a " digit " " c " " i " is not obtained from it by simply multiplying by a place value.
• The factorial number system is a mixed radix numeral system : the " i "-th digit from the right has base " i ", which means that the digit must be strictly less than " i ", and that ( taking into account the bases of the less significant digits ) its value to be multiplied by ! ( its place value ).
• Converting successive natural numbers to the factorial number system produces those sequences in lexicographic order ( as is the case with any mixed radix number system ), and further converting them to permutations preserves the lexicographic ordering, provided the Lehmer code interpretation is used ( using inversion tables, one gets a different ordering, where one starts by comparing permutations by the " place " of their entries 1 rather than by the value of their first entries ).