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IEEE Transactions on Information Theory, 2005 We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree.
Canteaut, Anne, Videau, Marion
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On circularly symmetric functions
Applied Mathematics Letters, 2010 AbstractIn this paper, we study the logarithmic coefficients of circularly symmetric functions. Also, we investigate the relative growth of successive coefficients of circularly symmetric functions. Furthermore, we obtain the sharp estimate for the order of ‖Dn|−|Dn−1‖ by using the method of the logarithmic coefficients.
Qin Deng
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Lipschitz symmetric functions on Banach spaces with symmetric bases
Karpatsʹkì Matematičnì Publìkacìï, 2021 We investigate Lipschitz symmetric functions on a Banach space $X$ with a symmetric basis. We consider power symmetric polynomials on $\ell_1$ and show that they are Lipschitz on the unbounded subset consisting of vectors $x\in \ell_1$ such that $|x_n ...
M.V. Martsinkiv +3 more
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Product of Stanley symmetric functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We study the problem of expanding the product of two Stanley symmetric functions $F_w·F_u$ into Stanley symmetric functions in some natural way. Our approach is to consider a Stanley symmetric function as a stabilized Schubert polynomial $F_w=\lim _n ...
Nan Li
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On the correlation of symmetric functions [PDF]
Mathematical Systems Theory, 1996 N ...
Cai, Jin-Yi +2 more
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Sensitivities and block sensitivities of elementary symmetric Boolean functions
Journal of Mathematical Cryptology, 2021 Boolean functions have important applications in molecular regulatory networks, engineering, cryptography, information technology, and computer science. Symmetric Boolean functions have received a lot of attention in several decades.
Zhang Jing, Li Yuan, Adeyeye John O.
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Symmetry Properties of Nested Canalyzing Functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Many researchers have studied symmetry properties of various Boolean functions. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used to model certain biological phenomena.
Daniel J. Rosenkrantz +3 more
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Immaculate basis of the non-commutative symmetric functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric ...
Chris Berg +4 more
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The symmetric KP hierarchy and affine Yangian of gl(1)
Nuclear Physics B, 2023 The symmetric functions Yλ(x) are a generalization of Schur functions Sλ(x), and Yλ(x) are symmetric about the x-axis and y-axis. As the Schur functions can be used to describe the tau functions of the KP hierarchy, in this paper, we define the symmetric
Na Wang, Ke Wu
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$H$-Chromatic Symmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2022 We introduce $H$-chromatic symmetric functions, $X_{G}^{H}$, which use the $H$-coloring of a graph $G$ to define a generalization of Stanley's chromatic symmetric functions. We say two graphs $G_1$ and $G_2$ are $H$-chromatically equivalent if $X_{G_1}^{H} = X_{G_2}^{H}$, and use this idea to study uniqueness results for $H$-chromatic symmetric ...
Nancy Mae Eagles +4 more
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