user avatar
user avatar
user avatar
linear_combinatori_probabi
  • Member for 5 years, 6 months
  • Last seen more than 1 year ago
Stats
1,432
reputation
123
reached
0
answers
2
questions
Loading…
About


Combinatorics I have been chasing for years: ($U$, the universe, is defined by $S_0$)

  • $\textrm{Exactly-IEP}_U(k)=\sum\limits_{j=k}^m(-1)^{j-k}\color{blue}{\binom{j}{k}}S_j.\quad$ // All I have for you is a word, TENET.
  • $\textrm{At_Least-IEP}_U(k)=\sum\limits_{j=k}^m(-1)^{j-k}\color{blue}{\binom{j-1}{j-k}}S_j.\quad$ // Pascal Explosion.

People proving it using mechanical-memory idea:

  • $\textrm{Let }m>k: \sum\limits_{l=0}^{k}\sum\limits_{j=l}^m=\sum\limits_{j=0}^m\sum\limits_{l=0}^{\min(j,k)}$ // Independentness of addition.
This user doesn’t have any gold badges yet.
5
silver badges
7
bronze badges
Top tags
0
Score
2
Posts
100
Posts %
0
Score
1
Posts
50
Posts %
0
Score
1
Posts
50
Posts %
0
Score
1
Posts
50
Posts %
0
Score
1
Posts
50
Posts %