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  1. How many ways can we get 2 a's and 2 b's from aabb?

    If I do this manually, it's clear to me the answer is 6, aabb abab abba baba bbaa baab Which is the same as \mathchoice((((4 2\mathchoice)))) \mathchoice ((((4 2 \mathchoice)))) But I don't really …

  2. Matrices - Conditions for $AB+BA=0$ - Mathematics Stack Exchange

    The Problem Let A A be the matrix (a c b d) (a b c d), where no one of a,b,c,d a, b, c, d is 0 0. Let B B be a 2×2 2 × 2 matrix such that AB+ BA= (0 0 0 0) A B + B ...

  3. sequences and series - The Perfect Sharing Algorithm (ABBABAAB ...

    Oct 4, 2016 · The algorithm is normally created by taking AB, then inverting each 2-state 'digit' and sticking it on the end (ABBA). You then take this entire sequence and repeat the process (ABBABAAB).

  4. How to calculate total combinations for AABB and ABBB sets?

    Apr 19, 2022 · Although both belong to a much broad combination of N=2 and n=4 (AAAA, ABBA, BBBB...), where order matters and repetition is allowed, both can be rearranged in different ways: …

  5. $A^2=AB+BA$. Prove that $\\det(AB-BA)=0$

    Let A, B A, B be two 3 × 3 3 × 3 matrices with complex entries, such that A2 = AB + BA A 2 = A B + B A. Prove that det(AB − BA) = 0 det (A B B A) = 0 Nice problem, and I want to find a solution. AB − BA = …

  6. (Jacobson Basic Algebra I) Exercise 1.2.7 (monoid inverse exercise)

    Feb 22, 2025 · I hadn't made the leap to realize that abba = 1 means that a is left/right invertible and therefore has an inverse, it's rather clever. Also thank you for the minimal counter example, it's very …

  7. How many words of length - Mathematics Stack Exchange

    {AABB, ABAB, ABBA, BBAA, BAAB, BABA} {A A B B, A B A B, A B B A, B B A A, B A A B, B A B A} So, I need to know what this w(n) = w(ni,nj) w (n) = w (n i, n j) is. Some references on aproaches on how …

  8. elementary number theory - Divisibility Tests for Palindromes ...

    The 4 4 -digit palindrome abba a b b a is divisible by 101 iff a = b a = b. The 5 5 -digit palindrome abcba a b c b a is divisible by 101 iff c = 2a c = 2 a. The 6 6 -digit palindrome abccba a b c c b a is divisible …

  9. CW complex for Möbius strip and its homeomorfisams

    Jan 14, 2023 · is attaching a map for ABBA. It is easy to see that these maps are continuous. And f(x) = x+1 2 f (x) = x + 1 2 for second 1-cell. Is this okey? According to this question, there is CW complex …

  10. How to show that - Mathematics Stack Exchange

    Jan 26, 2015 · Let A A and B B be two 3 × 3 3 × 3 matrices with complex entries such that A2 = AB + BA A 2 = A B + B A. Prove that det(AB − BA) = 0 det (A B B A) = 0. (Is the above result true for matrices …