A367432 Number of commutative discrete aggregation functions defined on the finite chain L_n={0,1,...,n-1,n} that are smooth.

1, 2, 10, 80, 1008, 19764, 600028, 28134464, 2034669118, 226781039624

Offset: 0

Author

Marc Munar, Nov 18 2023

Keywords

• nonn
• hard
• more

Comments

The number of smooth and commutative discrete aggregation functions on the finite chain L_n={0,1,...,n-1,n}, i.e., the number of monotonic increasing binary functions F: L_n^2->L_n such that F(0,0)=0 and F(n,n)=n, F(x,y)=F(y,x) for all x,y in L_n (commutativity), and F(x+1,y)-F(x,y)<=1 and F(y,x+1)-F(y,x)<=1 for all y in L_n and x in L_n\{n} (smooth).

Also, the number of (n+1)X(n+1) integer symmetric matrices (m_{i,j}) such that m_{1,1}=1, m_{n+1,n+1}=n+1, and all rows and columns are (weakly) monotonic without jumps larger than 1.

Crossrefs

Symmetric counterpart of matrices enumerated in A306372.

Smooth counterpart of operators defined in A366447.

Extensions

a(0) and a(7)-a(9) from Martin Ehrenstein, Dec 01 2023