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Ira Gessel
Ira Gessel
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Here is a "colourful" description of what I would like to count. Suppose you have one of those tables you see in a casino. I think they are for roulette, with $m$ squares, each of them with a number inside them. You have $c_1$chips chips of type 1, $c_2$ chips of type $2\dots$ $c_n$$2,\dots,c_n$ chips of type $n$. You have to place the chips on top of the squares such that each number has at least $1$ chip over it but no square has two or more chips of the same colour on top of it. In how many ways can we do this?

Here is a "colourful" description of what I would like to count. Suppose you have one of those tables you see in a casino. I think they are for roulette, with $m$ squares, each of them with a number inside them. You have $c_1$chips of type $c_2$ chips of type $2\dots$ $c_n$ chips of type $n$. You have to place the chips on top of the squares such that each number has at least $1$ chip over it but no square has two or more chips of the same colour on top of it. In how many ways can we do this?

Here is a "colourful" description of what I would like to count. Suppose you have one of those tables you see in a casino. I think they are for roulette, with $m$ squares, each of them with a number inside them. You have $c_1$ chips of type 1, $c_2$ chips of type $2,\dots,c_n$ chips of type $n$. You have to place the chips on top of the squares such that each number has at least $1$ chip over it but no square has two or more chips of the same colour on top of it. In how many ways can we do this?

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Gorka
Gorka
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How is this combinatorial structure called?

Here is a "colourful" description of what I would like to count. Suppose you have one of those tables you see in a casino. I think they are for roulette, with $m$ squares, each of them with a number inside them. You have $c_1$chips of type $c_2$ chips of type $2\dots$ $c_n$ chips of type $n$. You have to place the chips on top of the squares such that each number has at least $1$ chip over it but no square has two or more chips of the same colour on top of it. In how many ways can we do this?