AI 中文总结
研究偏斜汉明集对问题，通过基于特征二代数的线性代数方法，证明了\(m\leq2^{t + 1}\)的紧界，解决了相关问题。
AI 中文摘要
设\(X\)为字母表，\(t\geq0\)且\(n\geq t + 1\)，\(((a_i,b_i))_{i = 1}^{m}\)是\(X^n\)中满足对每个\(i\)有\(dist(a_i,b_i)\geq t + 1\)且\(i\lt j\)时\(dist(a_i,b_j)\leq t\)的有序单词对族。证明了紧界\(m\leq2^{t + 1}\)，解决了Alon、Jin和Sudakov提出的问题。证明采用基于特征二代数的线性代数方法，该方法可能具有独立价值。
英文摘要
Let $X$ be an alphabet, let $t\geq 0$ and $n\geq t+1$, and let $((a_i,b_i))_{i=1}^{m}$ be an ordered family of word pairs in $X^n$ satisfying $dist(a_i,b_i)\geq t+1$ for every $i$ and $dist(a_i,b_j)\leq t$ whenever $i<j$. We prove the sharp bound $m\leq 2^{t+1}$, thereby resolving a problem posed by Alon, Jin, and Sudakov. Our proof uses a linear-algebraic method based on a characteristic-two algebra, which may be of independent interest.
