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A092450 Triangle read by rows: T(m,n) = number of weak factorization systems (trivial Quillen model structures) on the product category [m]x[n], where [m] denotes the total order on m objects, viewed as a category. 2
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 5, 10, 5, 1, 1, 14, 68, 68, 14, 1, 1, 42, 544, 1396, 544, 42, 1, 1, 132, 4828, 37434, 37434, 4828, 132, 1, 1, 429, 46124, 1226228, 4073836, 1226228, 46124, 429, 1, 1, 1430, 465932, 47002628, 645463414, 645463414, 47002628 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Specifying a weak factorization system on a poset category is equivalent to specifying a set of morphisms that includes all identity morphisms and is closed under composition and pullback.

LINKS

Hugh Robinson, Table of n, a(n) for n = 0..69

Hugh Robinson, Haskell (ghc 7.4) program to generate the sequence

FORMULA

T(0, n) = T(n, 0) = 1. T(1, n) = T(n, 1) = C(n) the n-th Catalan number (A000108).

EXAMPLE

T(2, 2) = 10:  the category has five nonidentity morphisms with relations ca = db = e.  a is a pullback of d and of e;  b is a pullback of c and of e.  So there are ten allowable sets of morphisms:  omitting identities for brevity, they are {}, {a}, {b}, {a,b}, {b,c}, {a,d}, {a,b,e}, {a,b,c,e}, {a,b,d,e}, {a,b,c,d,e}.

CROSSREFS

Cf. A091378, A000108.

Sequence in context: A295690 A219727 A177694 * A279629 A014291 A136587

Adjacent sequences:  A092447 A092448 A092449 * A092451 A092452 A092453

KEYWORD

nonn,tabl

AUTHOR

Hugh Robinson, Mar 24 2004

EXTENSIONS

More terms from Hugh Robinson, Oct 02 2011

STATUS

approved

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Last modified August 22 17:23 EDT 2019. Contains 326180 sequences. (Running on oeis4.)