New answers tagged

2 votes

Counting $m\times n$ $\bigl({1\atop1}{1\atop0}\bigr)$-free $(0,1)$-matrices

Command Master has already answered the question nicely. For my own understanding, this answer works out the details of that answer in the $m=3$ case (excluding the linear algebra at the end). Here's ...
ho boon suan's user avatar
7 votes
Accepted

Counting $m\times n$ $\bigl({1\atop1}{1\atop0}\bigr)$-free $(0,1)$-matrices

We can show that for every $m$ there is a polynomial $q_m$ of degree $\binom m2$ such that $G_{m, n} = (m+1)^n q_m(n)$. We will do this by constructing a matrix $A_m$ such that $G_{m, n} = \mathbf{1} ...
Command Master's user avatar
1 vote
Accepted

Formula for partitions of integers with no subpartition being a partition of $t$

Let $t$ be fixed. Per Answer 1, the number of 2-forcing (nonnegative) partitions equals the coefficient of $q^M$ in Gaussian binomial coefficient $\binom{N+t-1}{N}_q$. To answer Question 1.5, it is ...
Max Alekseyev's user avatar

Top 50 recent answers are included