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Discussion
Over coffee, Bob said that he really liked this chapter. This material was full of cases of very concrete procedures for doing useful things. I like that.
Discussion
Over coffee, Bob said that he really liked this chapter. This material was full of cases of very concrete procedures for doing useful things. I like that. Yolanda offered a somewhat different perspective On the other hand, this last procedure only seems to work with interval orders and we still don't have a clue as to how to find the width of a poset in the general case. This might be very difficultlike the graph coloring problems discussed in the last chapter. Dave weighed in with Somehow I think there's going to be a fairly efficient process that works for all posets. We may not have all the tools yet, but let's wait a bit.
Not much was said for a while and after a pause, Carlos ventured that there were probably a lot of combinatorial problems for posets that had analogous versions for graphs and in those cases, the poset version would be a bit more complicated, sometime a little bit and sometimes a very big bit. Zori was quiet but she was thinking. These poset structures might even be useful, as she could imagine many settings in which a linear order was impossible or impractical. Maybe there were ways here to earn a few dollars.
Indi sen Hiç bir hasapçy buny çözmez, emma onuň bölekleri hasaplanmak üçindir. Aşakda birini synla ýa-da özüňi ýaz.
Şu ýerde ulanylan simwollar
Eň täze düşündirme, surat, we her harpyň manysy üçin her bir simwoly basyň.
Adamlar soraýan soraglar
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.
Bu sahypanyň käbir bölegi şundan alyndy Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Bu ýerde gysgaldylan we tekrar beýan edilen; hatalar biziňkidir.
_Ýaşa 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