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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 …

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

    As long as a, b, c a, b, c are not all 0 0, this has rank 2 2, so there is a 2 2 -dimensional linear space of B B for which AB + BA = 0 A B + B A = 0 in this case. On ...

  3. 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 …

  4. 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 …

  5. How many $4$-digit palindromes are divisible by $3$?

    Feb 28, 2018 · How many 4 4 -digit palindromes are divisible by 3 3? I'm trying to figure this one out. I know that if a number is divisible by 3 3, then the sum of its digits is divisible by 3 3. All I …

  6. 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 …

  7. (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 …

  8. prove $\\Gamma(a)\\Gamma(b) = \\Gamma(a+b)B(a,b)$ using …

    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 =

  9. 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 …

  10. 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 …