Changes between Initial Version and Version 1 of Ticket #16461, comment 19


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Timestamp:
06/11/14 16:14:29 (7 years ago)
Author:
vdelecroix
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  • Ticket #16461, comment 19

    initial v1  
    1212> As your function handles a lot of `l>1` already, what would you mean of changing the "if" into "`(v-1)%k == 0 and l%(k-1) == 0`" ? In which case we could return "several times the same difference family" if `l` is equal to `2(k-1)` ?
    1313
    14 Actually, it is more than that. You can take the union of several families with the same `(G,k)` (the group `G` need to be fixed). If you have `(G,k,l1)`, `(G,k,l2)`, ..., `(G,k,ln)` difference families then you have a `(G,k,l1+l2+...+ln)` by taking the union. In other words, the set of `l` you can build for a fixed `(G,k)` is a semi-group of the integers... it is more than just stable under multiplicative.
     14Actually, it is more than that. You can take the union of several families with the same `(G,k)` (the group `G` need to be fixed). If you have `(G,k,l1)`, `(G,k,l2)`, ..., `(G,k,ln)` difference families then you have a `(G,k,l1+l2+...+ln)` by taking the union. In other words, the set of `l` you can build for a fixed `(G,k)` is a semi-group of the integers... it is more than just stable under multiplication.