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Mathematics
[PAST EVENT] Honors Thesis Defense: Xiaonan Hu
April 27, 2016
11am - 12:30pm
Abstract:
A $letter~matrix$ is an $n$-by-$n$ matrix whose entries are $n$ symbols, each appearing $n$ times. The row (column) distribution of a letter matrix is an $n$-by-$n$ nonnegative integer matrix that tells how many of each letter are in each row (column). A row distribution $R$ and a column distribution $C$ are compatible if there exits a letter matrix $A$ whose row distribution is $R$ and whose column distribution is $C$. We show that the matrix $J$ of all ones is compatible with any $C$, and we also consider the the problem of when $R$ and $C$ pairs are compatible in terms of their values and patterns inside the distribution matrices.
A $letter~matrix$ is an $n$-by-$n$ matrix whose entries are $n$ symbols, each appearing $n$ times. The row (column) distribution of a letter matrix is an $n$-by-$n$ nonnegative integer matrix that tells how many of each letter are in each row (column). A row distribution $R$ and a column distribution $C$ are compatible if there exits a letter matrix $A$ whose row distribution is $R$ and whose column distribution is $C$. We show that the matrix $J$ of all ones is compatible with any $C$, and we also consider the the problem of when $R$ and $C$ pairs are compatible in terms of their values and patterns inside the distribution matrices.