MathOverflow

Motivation: As a personal side project I have been working with an inclusion-exclusion formulation that is counting weighted power’s $x^a$ between consecutive squares $[n^2, (n+1)^2]$. The function $f(x)$ however involves a lot of floor functions and...

Let $M = \begin{pmatrix} P & Q \\ R & S \end{pmatrix}, \quad P = M[X] \ (k\times k, \text{invertible}), \quad S = M[Y] \ ( (n-k)\times (n-k) ).$how to prove that $r( \begin{pmatrix} P^{-1}+I & -P^{-1}Q \\[2pt] RP^{-1} & S - RP^{-1}Q ...

In this paper, necessary and sufficient conditions for the determinacy of Borel games of length $\omega^2$ are given. Is it known whether ZFC establishes the determinacy of Borel games of length $\omega \cdot n$?

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Let $n \in \mathbb{N}$ and let $C > 0$ be a fixed constant. Consider the class of monic polynomials of degree $n$ with complex coefficients bounded by $C$:$$\mathcal{P}_n(C) = \left\{ P(z) = z^n + \sum_{j=0}^{n-1} a_j z^j \;\Bigg|\; a_j \in \mathbb...