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pro vyhledávání: '"RICE, ALEX"'
The Seidel matrix of a tournament on $n$ players is an $n\times n$ skew-symmetric matrix with entries in $\{0, 1, -1\}$ that encapsulates the outcomes of the games in the given tournament. It is known that the determinant of an $n\times n$ Seidel mat
Externí odkaz:
http://arxiv.org/abs/2406.09697
Autor:
Doyle, John R., Rice, Alex
We establish upper bounds on the size of the largest subset of $\{1,2,\dots,N\}$ lacking nonzero differences of the form $h(p_1,\dots,p_{\ell})$, where $h\in \mathbb{Z}[x_1,\dots,x_{\ell}]$ is a fixed polynomial satisfying appropriate conditions and
Externí odkaz:
http://arxiv.org/abs/2405.00868
Autor:
Clevenger, Ginny Ray, Havard, Haley, Heard, Patch, Lott, Andrew, Rice, Alex, Wilson, Brittany
For $A\subseteq \mathbb{R}$, let $A+A=\{a+b: a,b\in A\}$ and $AA=\{ab: a,b\in A\}$. For $k\in \mathbb{N}$, let $SP(k)$ denote the minimum value of $\max\{|A+A|, |AA|\}$ over all $A\subseteq \mathbb{N}$ with $|A|=k$. Here we establish $SP(k)=3k-3$ for
Externí odkaz:
http://arxiv.org/abs/2307.06874
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces desired stric
Externí odkaz:
http://arxiv.org/abs/2302.05303
Autor:
Agrawal, Raj, Bhatia, Prarthana, Gupta, Kratik, Lamb, Powers, Lott, Andrew, Rice, Alex, Ward, Christine Rose
A $\textit{covering system}$ is a collection of integer congruences such that every integer satisfies at least one congruence in the collection. A covering system is called $\textit{distinct}$ if all of its moduli are distinct. An expansive literatur
Externí odkaz:
http://arxiv.org/abs/2208.09720
Publikováno v:
In Linear Algebra and Its Applications 15 February 2025 707:126-151
Publikováno v:
Involve 15 (2022) 857-884
A standard proof of Schur's Theorem yields that any $r$-coloring of $\{1,2,\dots,R_r-1\}$ yields a monochromatic solution to $x+y=z$, where $R_r$ is the classical $r$-color Ramsey number, the minimum $N$ such that any $r$-coloring of a complete graph
Externí odkaz:
http://arxiv.org/abs/2112.03127
Autor:
Das, Anupam, Rice, Alex
Publikováno v:
Logical Methods in Computer Science, Volume 19, Issue 2 (May 19, 2023) lmcs:8695
A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. In this work we leverage recently developed graphical representations of linear formulae to build an implementation that is capable o
Externí odkaz:
http://arxiv.org/abs/2111.05209
Many definitions of weak and strict $\infty$-categories have been proposed. In this paper we present a definition for $\infty$-categories with strict associators, but which is otherwise fully weak. Our approach is based on the existing type theory Ca
Externí odkaz:
http://arxiv.org/abs/2109.01513
Autor:
Balaji, Vishal, Lamb, Powers, Lott, Andrew, Patel, Dhruv, Rice, Alex, Singh, Sakshi, Ward, Christine Rose
For integers $k,r\geq 2$, the diagonal Ramsey number $R_r(k)$ is the minimum $N\in\mathbb{N}$ such that every $r$-coloring of the edges of a complete graph on $N$ vertices yields on a monochromatic subgraph on $k$ vertices. Here we make a careful eff
Externí odkaz:
http://arxiv.org/abs/2108.08410