ar X iv : 0 81 1 . 19 83 v 1 [ m at h . C O ] 1 2 N ov 2 00 8 DIFFERENTIAL POSETS AND SMITH NORMAL FORMS
نویسنده
چکیده
We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU + tI and UD + tI have Smith normal forms over Z[t]. In particular, this would determine the integral structure of the maps U, D, UD, DU , including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice YF studied by Okada and its r-differential generalizations Z(r), as well as verifying many of its consequences for Young’s lattice Y and the r-differential Cartesian products Y r.
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