## New answers tagged enumerative-combinatorics

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 ...

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} ...

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 ...

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