[seqfan] Re: First difference of lexigraphical ordering of subsets of integers

[Neil Sloane]

Well, given S and k, there are binomial(n,k) subsets of size k, and the
length of the first-difference sequence is 1 less than that

I am not sure what you asking about - which sequence are you asking should
be in the OEIS?


Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Mon, Dec 2, 2019 at 10:44 PM Tommaso Martino <tommartin at hotmail.it>
wrote:

> Hello seqfans,
> this is my first attempt, so I hope to not get in wrong.
>
> Given S={1,2,3,4,5,6,7,8,9}, we can generate a finite sequence containing
> the lexicographical ordering of the subsets of k elements of S.
> We now define the new sequence a(n) as the first difference of such list,
> which is a(n+1)-a(n).
>
> -- Example 1.
> Given S, the lexicographical ordering on the subsets of 2 elements of S is:
>
>   12 13 14 15 16 17 18 19 23 24 25
>   26 27 28 29 34 35 36 37 38 39 45
>   46 47 48 49 56 57 58 59 67 68 69
>   78 79 89
>
> The first difference of the generated sequence is:
>
>   1  1  1  1  1  1  1  4
>   1  1  1  1  1  1  5
>   1  1  1  1  1  6
>   1  1  1  1  7
>   1  1  1  8
>   1  1  9
>   1  10
>
> -- Example 2.
> Given S, the lexicographical ordering on the subsets of 3 elements of S is:
>
>   123 124 125 126 127 128 129 134 135 136 137 138 139 145 146 147 148 149
>   156 157 158 159 167 168 169 178 179 189 234 235 236 237 238 239 245 246
>   247 248 249 256 257 258 259 267 268 269 278 279 289 345 346 347 348 349
>   356 357 358 359 367 368 369 378 379 389 456 457 458 459 467 468 469 478
>   479 489 567 568 569 578 579 589 678 679 689 789
>
> The first difference of the generated sequence is:
>
>   1   1   1   1   1   1
>   5   1   1   1   1   1
>   6   1   1   1   1   7
>   1   1   1   8   1   1
>   9   1  10  45   1   1
>   1   1   1   6   1   1
>   1   1   7   1   1   1
>   8   1   1   9   1  10
>   56  1   1   1   1   7
>   1   1   1   8   1   1
>   9   1  10  67   1   1
>   1   8   1   1   9   1
>   10  78  1   1   9   1
>   10  89  1  10 100
>
> Some repeating pattern seems to appear in the sequence.
> Different sequences can be generated with the same S, and increasing
> values of k < S.
> The length of the sequence can be easily computed, and it is a function of
> both k and S.
> Modifying the length of S, for example S={2..8}, different sequences can
> be obtained.
>
> Is it worth submitting to OEIS?
>
> Thank you,
> Tommaso MARTINO
>
> --
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>