Tootfinder

This https://arxiv.org/abs/2501.16144 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Survey of the Holroyd-Talbot Conjecture
A family of sets is intersecting if every pair of its members has an element in common. Such a family of sets is called a star if some element is in every set of the family. Given a graph $G$, let $μ(G)$ denote the size of the smallest maximal independent set of $G$. In 2005, Holroyd and Talbot conjectured the following generalization of the Erdős-Ko-Rado Theorem: for $1\le r\le μ(G)/2$, there is a maximum size intersecting family of independent $r$-sets that is a star. In this paper we pres…

This https://arxiv.org/abs/2407.13450 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sparse Nullstellensatz, resultants and determinants of complexes
We refine and extend a result by Tuitman on the supports of a Bezout identity satisfied by a finite sequence of sparse Laurent polynomials without common zeroes in the toric variety associated to their supports. When the number of these polynomials is one more than the dimension of the ambient space, we obtain a formula for computing the sparse resultant as the determinant of a Koszul type complex.

This https://arxiv.org/abs/2410.20448 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New results related to cutters and to an extrapolated block-iterative method for finding a common fixed point of a collection of them
Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous applications in science and engineering. We consider an extrapolated block-iterative method with dynamic weights for solving the CFPP assuming the operators belong to a wide class of operators called cutters. Global convergence is proved in two different scenari…

This https://arxiv.org/abs/2503.11463 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sorting permutations with pile shuffle on queue-like and stack-like piles
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we formalize the pile shuffle and investigate its capabilities as a sorting device. Our study is novel in that we consider pile shuffle in three variations: (1) using queue-like piles, (2) using stack-like piles, and (3) using a heterogeneous mixture of those two pile types, either given or decided during the shuffle by the dealer herself. We first characterize the sortable permutations of one or more sequ…

This https://arxiv.org/abs/2410.20448 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New results related to cutters and to an extrapolated block-iterative method for finding a common fixed point of a collection of them
Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous applications in science and engineering. We consider an extrapolated block-iterative method with dynamic weights for solving the CFPP assuming the operators belong to a wide class of operators called cutters. Global convergence is proved in two different scenari…

This https://arxiv.org/abs/2408.00810 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound
We introduce the notion of p-adic equiangular lines and derive the first fundamental relation between common angle, dimension of the space and the number of lines. More precisely, we show that if $\{τ_j\}_{j=1}^n$ is p-adic $γ$-equiangular lines in $\mathbb{Q}^d_p$, then \begin{align*} (1) \quad\quad \quad \quad |n|^2\leq |d|\max\{|n|, γ^2 \}. \end{align*} We call Inequality (1) as the p-adic van Lint-Seidel relative bound. We believe that this complements funda…

This https://arxiv.org/abs/2501.03645 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Big convex polytopes or rich hyperplanes
For natural numbers $n$ and $l > d \geq 2$, let $ES_d(l,n)$ be the minimum $N$ such that any set of at least $N$ points in $\mathbb{R}^d$ contains either $l$ points contained in a common $(d-1)$-dimensional hyperplane or $n$ points in convex position. In this paper, we give the upper and lower bounds for $ES_d(l,n)$.

This https://arxiv.org/abs/2505.02678 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

Why is the volatility of single stocks so much rougher than that of the S&P500?
The Nested factor model was introduced by Chicheportiche et al. to represent non-linear correlations between stocks. Stock returns are explained by a standard factor model, but the (log)-volatilities of factors and residuals are themselves decomposed into factor modes, with a common dominant volatility mode affecting both market and sector factors but also residuals. Here, we consider the case of a single factor where the only dominant log-volatility mode is rough, with a Hurst exponent $H \sim…