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Discussion
After studying the proof that the number of partitions of an integer into odd parts is the same as the number of partitions of that integer into distinct parts, Yolanda was beside herself.
Discussion
After studying the proof that the number of partitions of an integer into odd parts is the same as the number of partitions of that integer into distinct parts, Yolanda was beside herself. Do you guys realize what we just did? We showed that two quantities were equal without saying anything about what those quantities actually were. That's really neat, she said. Nobody said anything for a long time, but after some time Dave said There might be other instances where you would want to be able to communicate fully, yet hold back on every last detail. Bob said I don't get it. Alice interjected a comment that was more of question than a statement Do you mean that parties may want to communicate, while maintaining that the conversation did not occur? Carlos added Or maybe they just want to be able to detect whether anyone else was listening. Now Zori was nearly happy. Privacy and security were big ticket items.
Ngayon ikaw Walang kalkulador settles ito isa, ngunit ang mga piraso ng mga ito ay computable. Subukan ang isa sa ibaba, o type ang iyong sarili.
Ang isang libreng account ay nagdaragdag ng mga tala sa bawat aralin, isang tala ng kung ano ang iyong natapos, ang iyong mga nalulutas na problema sa isang lugar, at isang guro na maaari mong tanungin tungkol sa pahinang ito. Ang matematika mismo ay bukas sa lahat, naka-sign in o hindi.
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Permutation or combination?
Ask whether order matters. A lock code is a permutation (order matters); a hand of cards is a combination (it does not).
What is a graph in this sense?
Dots (vertices) joined by lines (edges), not a plot. Road maps, social networks and molecules are graphs; questions like "is there a route" and "how few colours" are graph theory.
Bahagi ng pahinang ito ay naaayon mula sa Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Condensed at muling ipinaliwanag dito; errors ay aming.
Higit pa sa Combinatorics & Graph Theory
The counting principlesPigeonhole principle and inclusion, exclusionBinomial coefficients and Pascal's triangleRecurrences and generating functionsGraphs: vertices, edges, degreesPaths, cycles, trees, Euler and HamiltonColouring and planar graphs