![]() So the range is all sets with $k$ elements, i.e., n choose k elements. Each sequence uniquely determines the subset of the students who will get a prize.įor a), let's say that $n=2$, so you have the following binary strings: $\$ will be the only element of the restriction $f$ by $S_k$). So for example if the line has $n=5$ students, $01101$ means the first student won't get a prize, the next two will, and so on. You write down a sequence of $0$'s and/or $1$'s to record which students will get a prize. You decide to choose "some" of them (possibly all, possibly none) to get a prize. If you are not hungry, you are a teacher. For (d), how many ways are there to choose $k$ items for your meal, from the $n$ items available? (That includes the empty meal.)įor (c), a sequence is in $S_k$ if and only if you have decided to have a $k$-item meal. Note that the sequence $00000$ is a valid one: maybe you are on a diet.Įvery sequence of $n$ $0$'s and or $1$'s represents a choice of meal. So for example if $n=5$, and you write the sequence $01101$, that means you plan to say no to Item $1$, yes to Items $2$ and $3$, no to $4$, and yes to $5$. You decide to plan lunch ahead of time, by writing down a sequence of $0$'s and/or $1$'s. You are allowed to put on your tray $0$ or $1$ Type $1$ items, $0$ or $1$ type $2$ items, and so on. There is one Type $1$ item left, and one Type $2$ item, and one Type $3$ item, and so on up to one Type $n$ item. C 29, 1850074.Hint: You are in a cafeteria, at the end of the lunch hour. “ A self-updating digital chaotic stream cipher,” Int. “ Design of a hybrid model for construction of digital chaos and local synchronization,” Appl. “ A novel detection of periodic phenomena of binary chaotic sequences,” Acta Phys. “ A one-way coupled chaotic map lattice based self-synchronizing stream cipher,” Commun. ![]() “ Adaptive chaotic maps and their application to pseudo-random numbers generation,” Chaos Solit. “ An algorithm for the k-error linear complexity of binary sequences with period 2 n ,” IEEE Trans. “ A statistical test suite for random and pseudorandom number generators for cryptographic applications,” Appl. Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., Dray, J.“ Approximate entropy as measure of system complexity,” Proc. “ Cycle lengths and correlation properties of finite precision chaotic maps,” Int. The simplest representation consists of an electrical current or voltage, which is either on or off. “ The stability of the lattice structure of pseudorandom number sequences,” IEICE Trans. The binary sequence to be transmitted is usually available in the form of an electrical signal taking one between two random discrete values. “ Designing multi-dimensional logistic map with fixed-point finite precision,” Nonlin. “ Simple mathematical models with very complicated dynamics,” Nature 261, 459–467. “ Reducing the dynamical degradation by bi-coupling digital chaotic maps,” Int. “Dynamic analysis of digital chaotic maps via state-mapping networks,” IEEE Trans. “ TestU01: A C library for empirical testing of random number generators,” ACM Trans. “ Design and analysis of two stream ciphers based on chaotic coupling and multiplexing techniques,” Multimed. Jallouli, O., El Assad, S., Chetto, M.“ Chaos-based bitwise dynamical pseudorandom number generator on FPGA,” IEEE Trans. Garcia-Bosque, M., Perez-Resa, A., Sanchez-Azqueta, C., Aldea, C.“ A novel algorithm for detection and localization of periodic phenomena of chaotic binary sequences,” Int. “ Counteracting the dynamical degradation of digital chaos by applying stochastic jump of chaotic orbits,” Int. “ Nonlinear dynamics and chaos in a simplified memristor-based fractional-order neural network with discontinuous memductance function,” Nonlin. “ Periodicity detection in time series databases,” IEEE Trans. “ A general hybrid model for chaos robust synchronization and degradation reduction,” Inform. “ Dynamical analysis of a new multistable chaotic system with hidden attractor: Antimonotonicity, coexisting multiple attractors, and offset boosting,” Phys.
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