factorial number system造句

• 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 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 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.
• 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.
• 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.
• 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 ).