https://math.codidact.com/categories/41/tags/5409.rssNew Posts Tagged 'combinatorics' - MathematicsMathematics - Codidact2024-01-05T00:33:56Zhttps://math.codidact.com/posts/290492Is there a $(n_3)$ configuration which is not self-dual?WheatWizardhttps://math.codidact.com/users/543162024-01-04T03:47:14Z2024-01-05T00:33:56Z<p>Coxeter points out that for a self-dual configuration $(m_c,n_d)$ it must be that $m=n$ and $c=d$, so we may abbreviate it $(m_c)$.</p>
<p>However I'm interested in the other direction of this ...https://math.codidact.com/posts/289532Without trial and error, how can I effortlessly deduce all $n, k_i ∈ ℕ ∋ \binom n {k_1, k_2, ..., k_n} =$ given c? Chgg Clouhttps://math.codidact.com/users/535642023-08-25T10:37:06Z2023-08-26T04:37:14Z<h4>With online or computer software, for a given $c ∈ ℕ $, how can I efficiently deduce all natural numbers that $n, k_i ∈ ℕ ∋ \dbinom n { k_1, k_2, ..., k_i} = c$ ? For example below, $i = 1, \co...https://math.codidact.com/posts/286991organizing a librarymsh210https://math.codidact.com/users/81062022-09-12T15:36:11Z2022-09-13T05:58:16Z<p>Suppose you have $n>1$ books lined up on a shelf, numbered $1$ to $n$, not in the correct order, and you wish to put them in order. Here's your method: Choose a misplaced book<sup>[1]</sup> a...https://math.codidact.com/posts/286655Do the Faber partition polynomials have integer coefficients?Peter Taylorhttps://math.codidact.com/users/363562022-06-30T17:23:47Z2022-06-30T17:58:06Z<p>The Online Encyclopedia of Integer Sequences includes <a href="https://oeis.org/A263916">A263916: Coefficients of the Faber partition polynomials</a>. Perhaps the clearest definition given is</p...https://math.codidact.com/posts/285679How to intuit, construe multiplicands and multiplicators $\le 10$ resulting from $\dbinom pc$, WITHOUT division or factorials?DNBhttps://math.codidact.com/users/536282022-01-25T05:46:05Z2022-02-01T10:24:37Z<p>I grok, am NOT asking about, the answers below. Rather — <strong>how can I deduce and intuit the multiplicands and multiplicators $\le 10$, resulting from simplifying $\dbinom {p \text{ people...https://math.codidact.com/posts/285672To correct for overcounting, why can't we divide by the sum of the over-counts?DNBhttps://math.codidact.com/users/536282022-01-24T08:02:35Z2022-01-24T08:52:47Z<p>The book doesn't expatiate the sentence underlined in red below. 1. Why "it isn't 2 + 2"?</p>
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<li>Note that $2 \times 2 = 2 + 2 = 4$! Is this a coincidence?</li>
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<blockq...https://math.codidact.com/posts/285524How's it possible to arrange 0 objects? How can 0! = 1?DNBhttps://math.codidact.com/users/536282022-01-10T00:06:59Z2022-01-12T16:28:38Z<ol>
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<p>I don't understand the following explanation. Isn't it physically impossible to "arrange 0 objects", or nothing? It's senseless to raise the concept of arrangement when you have not...https://math.codidact.com/posts/284738Can the bijection for the Lost Boarding Pass Probability Problem, be formulated or pictured?DNBhttps://math.codidact.com/users/536282021-11-01T10:12:50Z2021-11-01T18:48:36Z<p>The two proofs below moot "bijection", but I don't see a formula. 1. Does the bijection have an explicit formula?</p>
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<li>Can this bijection be pictorialized? My 16 y.o. kid doe...https://math.codidact.com/posts/284651What does the distribution of a strictly increasing random walk look like if you stop at `N` steps?SherlockSagehttps://math.codidact.com/users/537952021-10-22T13:48:49Z2021-10-22T14:26:48Z<p>I have a puzzle inspired by the game Idle Brick Breaker (<a href="https://play.google.com/store/apps/details?id=com.TechTreeGames.IdleBrickBreaker&hl=en&gl=US">Google Play</a> and <a hre...https://math.codidact.com/posts/282642$\sum_{k=0}^{n} \binom{n}{k}=2^{n} \overset{?}{\iff} \sum_{k=0}^{n} \binom{2n+1}{k}=2^{2n}$DNBhttps://math.codidact.com/users/536282021-07-11T05:48:01Z2021-07-17T05:04:50Z<p><a href="https://math.stackexchange.com/a/2327533">Jack D'Aurizio narratively proved</a> $\color{red}{\sum\limits_{k=0}^{n} \binom{2n+1}{k}=2^{2n}}$. Is this red equation related, and can it b...https://math.codidact.com/posts/282611What's the bijection between Stars and Bars and Integer Solutions to an Equality? DNBhttps://math.codidact.com/users/536282021-07-09T05:52:06Z2021-07-09T05:52:06Z<p>The second quotation below keeps mentioning "bijection", but it never explicitly defines it. So what's the formula for that bijection?</p>
<p><a href="https://blogs.adelaide.edu.au/maths-learni...https://math.codidact.com/posts/282609Are Stars and Bars in Combinatorics related to the Fence Post Error?DNBhttps://math.codidact.com/users/536282021-07-09T05:28:13Z2021-07-09T05:28:13Z<p>The bars in the lower picture look like fences. That's why Stars and Bars reminds me of <a href="https://en.wikipedia.org/wiki/Off-by-one_error#Fencepost_error">Fence Post Error</a>?</p>
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