ISSN:
1572-9273
Keywords:
diagonal orders
;
planetrees
;
polynomial orders
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Here, N is the set of nonnegative integers, while an order in N n is a bijective function α : N n → N. Two orders are equivalent if they differ only by a permutation of their arguments. Let s(x)=x1+ ··· +x n for 0 〈 n ∈ N and x =(x 1, ···, x n ) ∈ N n ; such an α is a diagonal order if α(x) 〈 α(y) whenever x,y ∈ N n , and s(x) 〈 s(y). Lew composed Skolem"s diagonal polynomial orders to construct c n inequivalent nondiagonal polynomial orders in N n . Afterwards, Morales and Lew did the same with respect to the Morales–Lew"s diagonal orders, obtaining additional d n inequivalent nondiagonal polynomial orders. Moreover, they proved that d n / c n → ∞ as n → ∞. Recently, Sanchez obtained a family of (n − 1) ! inequivalent diagonal orders in N n . In this paper, we compose the Sanchez diagonal polynomial orders to construct e n inequivalent nondiagonal polynomial orders with e n ∼ e(n − 1) !, where e is the base of natural logarithms. Furthermore, we prove that e n / d n → ∞ as n → ∞.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006329224202
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