A Note on a Conjecture Concerning Symmetric Resilient Functions
نویسندگان
چکیده
In 1985, Chor et al 2] conjectured that the only 1-resilient symmetric functions are the exclusive-or of all n variables and its negation. In this note the existence of symmetric resilient functions is shown to be equivalent to the existence of a solution to a simultaneous subset sum problem. Then, using arithmetic properties of certain binomial coeecients, an innnite class of counterexamples to the conjecture is obtained.
منابع مشابه
An in nite class of counterexamples to a conjecture concerning non-linear resilient functions
The main construction for resilient functions uses linear error-correcting codes; a resilient function constructed in this way is said to be linear. It has been conjectured that if there exists a resilient function, then there exists a linear function with the same parameters. In this note, we construct innnite classes of non-linear resilient functions from the Kerdock and Preparata codes. We a...
متن کاملA note on Fouquet-Vanherpe’s question and Fulkerson conjecture
The excessive index of a bridgeless cubic graph $G$ is the least integer $k$, such that $G$ can be covered by $k$ perfect matchings. An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless cubic graph has excessive index at most five. Clearly, Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5, so Fouquet and Vanherpe as...
متن کاملA Further Note on Runs in Independent Sequences
Given a sequence of letters generated independently from a finite alphabet, we consider the case when more than one, but not all, letters are generated with the highest probability. The length of the longest run of any of these letters is shown to be one greater than the length of the longest run in a particular state of an associated Markov chain. Using results of Foulser and Karlin (19...
متن کاملOn a conjecture of Stanley on Jack symmetric functions
Koike, K., On a conjecture of Stanley on Jack symmetric functions, Discrete Mathematics 115 (1993) 211-216. The Jack symmetric function J,(x; G() is a symmetric function with interesting properties that J,(x; 2) is a spherical function of the symmetric pair (GL(n, FQ O(n, [w)) and that J,(x; 1) is the Schur function S,(x). Many interesting conjectures about the combinatorial properties of J,(x;...
متن کاملA Note on the Cone Restriction Conjecture in the Cylindrically Symmetric Case
Abstract. In this note, we present two arguments showing that the classical linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under the spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the second follows from a strengthening version of the Hausdorff-Young inequality and the Hölder inequal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Inf. Process. Lett.
دوره 47 شماره
صفحات -
تاریخ انتشار 1993