A030662 -id:A030662 - cp's OEIS frontend

A271219 Number n of antichains of P(En) x En, ordered by lexicographic order, with En a poset of n elements with no pair of elements ordered, and with En that same set augmented with an (n+1)th element smaller than all others.

1, 5, 83, 28925, 7663696588

Offset: 0

Emmanuel Chemla, Apr 02 2016

This sequence is, more interestingly, the number of logical consequence relations in (n+2)-valued logic, with no order between intermediate values (i.e., values other than 0 and 1), which are truth functional, identical to the standard logical consequence relation on bivalent propositions and value-monotonic (if the relation holds, it is preserved with stronger premises and/or weaker conclusions). See reference below.

In n-valued logic with all truth values strictly ordered, the number of logical consequence relations with the same properties is more standard, it corresponds to: A030662. It satisfies the same definition as this sequence except that En should now be understood as a well-ordered set of n elements.

E. Chemla, P. Egré and B. Spector, Characterizing logical consequence in many-valued logics, Ms. CNRS/ENS. J. of Logic and Computation, to appear (2016).

A300051 Triangle read by rows giving numbers T(n,j) (n >= 0, 1 <= j <= n+1) of certain restricted partitions of 2n into j blocks.

Original entry on oeis.org

1, 1, 1, 1, 5, 2, 1, 19, 24, 5, 1, 69, 202, 112, 14, 1, 251, 1520, 1665, 510, 42, 1, 923, 11000, 21121, 11827, 2277, 132, 1, 3431, 78806, 249137, 226205, 76111, 10010, 429, 1, 12869, 566234, 2840928, 3918842, 2044444, 456456, 43472, 1430

Offset: 0

Michael De Vlieger and N. J. A. Sloane, Feb 23 2018

See Vargas (2017) for a more precise definition.

			Triangle begins:
  1;
  1,   1;
  1,   5,     2;
  1,  19,    24,     5;
  1,  69,   202,   112,    14;
  1, 251,  1520,  1665,   510,   42;
  1, 923, 11000, 21121, 11827, 2277, 132;
  ...

Jorge Garza Vargas, The traffic distribution of the squared unimodular random matrix and a formula for the moments of its ESD, arXiv:1709.01498 [math.PR], 2017. See Table 1.

Main diagonal gives A000108.

Columns j=1-2 give: A000012, A030662.

The authors report that they were unable to find a general formula.

cp's OEIS Frontend

A271219 Number n of antichains of P(En) x En, ordered by lexicographic order, with En a poset of n elements with no pair of elements ordered, and with En that same set augmented with an (n+1)th element smaller than all others.

Views

Author

Keywords

Comments

Links

A300051 Triangle read by rows giving numbers T(n,j) (n >= 0, 1 <= j <= n+1) of certain restricted partitions of 2n into j blocks.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

cp's OEIS Frontend

A271219 Number n of antichains of P(En) x En*, ordered by lexicographic order, with En a poset of n elements with no pair of elements ordered, and with En* that same set augmented with an (n+1)th element smaller than all others.

Views

Author

Keywords

Comments

Links

A300051 Triangle read by rows giving numbers T(n,j) (n >= 0, 1 <= j <= n+1) of certain restricted partitions of 2n into j blocks.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A271219 Number n of antichains of P(En) x En, ordered by lexicographic order, with En a poset of n elements with no pair of elements ordered, and with En that same set augmented with an (n+1)th element smaller than all others.