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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. 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 …

  6. $A^2=AB+BA$. 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 = …

  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. 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 …

  9. The commutator of two matrices - Mathematics Stack Exchange

    The commutator [X, Y] of two matrices is defined by the equation $$\begin {align} [X, Y] = XY − YX. \end {align}$$ Two anti-commuting matrices A and B satisfy $$\begin {align} A^2=I \qu...

  10. prove $\\Gamma(a)\\Gamma(b) = \\Gamma(a+b)B(a,b)$ using polar ...

    Jun 23, 2022 · Question: prove Γ(a)Γ(b) = Γ(a + b)B(a, b) Γ (a) Γ (b) = Γ (a + b) B (a, b) using polar transformation: my attempt: L.H.S =