منابع مشابه
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A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up t...
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algebra is a theoretical course: we wonder more about why things are true than about how we can do things. Algebraists can at times be concerned more with elegance and beauty than applicability and efficiency. You may be tempted on many occasions to ask yourself the point of all this abstraction and theory. Who needs this stuff? Keep the examples above in mind; they show that algebra is not onl...
متن کاملClassifying APN Monomials
I present some results towards a classification of APN monomials. Such functions are useful as S-boxes in AES-like cryptosystems. An easy application of Weil’s theorem on absolutely irreducible curves shows that a monomial fm(x) = x m is not APN over F2n for all sufficiently large n if a related polynomial has absolutely irreducible factors over F2. This can help classify the APN families of mo...
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Young flattenings, introduced by Landsberg and Ottaviani, give determinantal equations for secant varieties and provide lower bounds for border ranks of tensors. We find special monomial-optimal Young flattenings that provide the best possible lower bound for all monomials up to degree 6. For degree 7 and higher these flattenings no longer suffice for all monomials. To overcome this problem we ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2005
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-005-4531-6