Let C_4,4(n,k) be the composition-counting function. Red-cell recurrence conjecture. C_4,4(5+k,2+k)= 12 & k=0, C_4,4(4+k,1+k)+14+4k & k>0. This conjecturally describes the red cells in Table 4; no proof or resolution is supplied.

Conjectured recurrence for the red cells of $C_{4,4}$

At least 7 years old · documented by 2018

Let $C_{4,4}(n,k)$ be the composition-counting function. Red-cell recurrence conjecture.

C_{4,4}(5+k,2+k)= \begin{cases} 12 & k=0,\\ C_{4,4}(4+k,1+k)+14+4k & k>0. \end{cases}

This conjecturally describes the red cells in Table 4; no proof or resolution is supplied.

References

Primary source

Vincent E. Coll,, Aria Dougherty, Matthew Hyatt, Andrew W. Mayers and Nick W. Mayers, “On compositions associated to seasweed subalgebras of sl(n)”, arXiv:1808.01008 (2018).

combinatorics seaweed-algebras

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