In this paper, a family of non-monomial permutations over the finite field F2n with differential uniformity at most 6 is proposed, where n is a positive integer. The algebraic degree of these functions is also determi...In this paper, a family of non-monomial permutations over the finite field F2n with differential uniformity at most 6 is proposed, where n is a positive integer. The algebraic degree of these functions is also determined.展开更多
Let uk （2, r） be a little q-Schur algebra over k, where k is a field containing an ι＇-th primitive root ε of 1 with ι＇〉 4 even, the author constructs a certain monomial base for little q-Schur algebra uk （2...Let uk （2, r） be a little q-Schur algebra over k, where k is a field containing an ι＇-th primitive root ε of 1 with ι＇〉 4 even, the author constructs a certain monomial base for little q-Schur algebra uk （2, r）.展开更多
Some techniques using linear algebra was introduced by Faugore in F4 to speed up the reduction process during Grobner basis computations. These techniques can also be used in fast implementations of F5 and some other ...Some techniques using linear algebra was introduced by Faugore in F4 to speed up the reduction process during Grobner basis computations. These techniques can also be used in fast implementations of F5 and some other signature-based Grobner basis algorithms. When these techniques are applied, a very important step is constructing matrices from critical pairs and existing polynomials by the Symbolic Preprocessing function （given in F4）. Since multiplications of monomials and polynomials are involved in the Symbolic Preprocessing function, this step can be very costly when the number of involved polynomials/monomials is huge. In this paper, multiplications of monomials and polynomials for a Boolean polynomial ring are investigated and a specific method of implementing the Symbolic Preprocessing function over Boolean polynomial rings is reported. Many examples have been tested by using this method, and the experimental data shows that the new method is very efficient.展开更多
Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.
It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterat...It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.展开更多
For a quantized enveloping algebra of finite type, one can associate a natural monomial to a dominant weight. We show that these monomials for types A5 and D4 are semitight(i.e., a Z-linear combination of elements in ...For a quantized enveloping algebra of finite type, one can associate a natural monomial to a dominant weight. We show that these monomials for types A5 and D4 are semitight(i.e., a Z-linear combination of elements in the canonical basis) by a direct calculation.展开更多
基金supported by the National Science Foundation of China under Grant Nos.11401172 and 61672212
文摘In this paper, a family of non-monomial permutations over the finite field F2n with differential uniformity at most 6 is proposed, where n is a positive integer. The algebraic degree of these functions is also determined.
文摘Let uk （2, r） be a little q-Schur algebra over k, where k is a field containing an ι＇-th primitive root ε of 1 with ι＇〉 4 even, the author constructs a certain monomial base for little q-Schur algebra uk （2, r）.
基金supported by the National Key Basic Research Program of China under Grant Nos.2013CB834203 and 2011CB302400the National Nature Science Foundation of China under Grant Nos.11301523,11371356,61121062+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDA06010701IEE’s Research Project on Cryptography under Grant Nos.Y3Z0013102,Y3Z0018102,and Y4Z0061A02
文摘Some techniques using linear algebra was introduced by Faugore in F4 to speed up the reduction process during Grobner basis computations. These techniques can also be used in fast implementations of F5 and some other signature-based Grobner basis algorithms. When these techniques are applied, a very important step is constructing matrices from critical pairs and existing polynomials by the Symbolic Preprocessing function （given in F4）. Since multiplications of monomials and polynomials are involved in the Symbolic Preprocessing function, this step can be very costly when the number of involved polynomials/monomials is huge. In this paper, multiplications of monomials and polynomials for a Boolean polynomial ring are investigated and a specific method of implementing the Symbolic Preprocessing function over Boolean polynomial rings is reported. Many examples have been tested by using this method, and the experimental data shows that the new method is very efficient.
基金supported by National Natural Science Foundation of China (Grant No.10771182)Doctorate Foundation Ministry of Education of China (Grant No. 200811170001)
文摘Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.
基金supported by the National Basic Research Program of China (Grant No. 2011CB302402)National Natural Science Foundation of China (Grant Nos. 61021004 and 10825104)Shanghai Leading Academic Discipline Project (Grant No. B412)
文摘It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.
文摘For a quantized enveloping algebra of finite type, one can associate a natural monomial to a dominant weight. We show that these monomials for types A5 and D4 are semitight(i.e., a Z-linear combination of elements in the canonical basis) by a direct calculation.
