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What is combinatorics? - Mathematics Stack Exchange In fact,I once tried to define combinatorics in one sentence on Math Overflow this way and was vilified for omitting infinite combinatorics I personally don't consider this kind of mathematics to be combinatorics, but set theory It's a good illustration of what the problems attempting to define combinatorial analysis are
combinatorics - What is a combinatorial proof exactly? - Mathematics . . . Combinatorics is a wide branch in Math, and a proof based on Combinatorial arguments can use many various tools, such as Bijection, Double Counting, Block Walking, et cetera, so a combinatorial proof may involve any (or a combination) of these
combinatorics - Why are the formulae related to circular permutations . . . Circular permutations Consider an arrangement of blue, cyan, green, yellow, red, and magenta beads in a circle For this particular arrangement of the six beads, there are six ways to list the arrangement of the beads in counterclockwise order, depending on whether we start the list with the blue, cyan, green, yellow, red, or magenta bead They correspond to the six linear arrangements shown
combinatorics - Formula for Combinations With Replacement - Mathematics . . . If you want a slightly more detailed explanation and exercises I recommend the book Introduction to Combinatorics published by the United Kingdom Mathematics Trust (UKMT) available at their webpage It covers many interesting topics with a problem solving approach to them
combinatorics - How To Tell When Order Matters Or Not - Mathematics . . . Comically badly worded question - particularly amusing is the phrase 'each card displays one positive integer without repetition from this set' :) it's almost like the output of a bot fed elementary combinatorics questions!
combinatorics - Why is $2^n$ considered to be all the possible . . . To reiterate $2^n-1$ is a fine answer to its own question the question of how many non-empty subsets a set has $2^n$ is a fine answer to its own question the question of how many subsets (empty or not) a set has Do not confuse the questions and do not immediately discount the one or the other as being unworthy of being asked or discussed