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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.
አሁን ምንም ዓይነት መሳሪያ ይህን አይቆጣጠርም፤ ነገር ግን ክፍሎቹ ሊቆጠሩ ይችላሉ። በታች ያለውን ይሞክሩ ወይም የራሳችሁን ይጻፉ።
ፊደላት
ለሙሉ መግለጫ፣ ምስል፣ እና በውስጡ ያለውን ፊደል ትርጓሜ ለማየት ማንኛውንም ምልክት ይጫኑ።
ጥያቄዎች
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.
የዚህ ገጽ ክፍሎች ከ Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). እዚህ የተቀረጸና የተተረጎመ፤ ስህተቶች የእኛ ናቸው፡፡
በ 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