Mersenne banner
no. 2
Computing r-removed P-orderings and P-orderings of order h
Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 33-40.

We develop a recursive method for computing the r-removed P-orderings and P-orderings of order h, the characteristic sequences associated to these and limits associated to these sequences for subsets S of a Dedekind domain D. This method is applied to compute these objects for S=ℤ and S=ℤ∖pℤ.

Publié le : 2011-10-20
DOI : https://doi.org/10.5802/acirm.31
Classification : 13F20,  11C08,  11S05,  13B25
Mots clés: integer valued polynomials, p-orderings, p-sequence, divided differences, finite differences 
@article{ACIRM_2010__2_2_33_0,
     author = {Keith Johnson},
     title = {Computing $r$-removed $P$-orderings and $P$-orderings of order $h$},
     journal = {Actes des rencontres du CIRM},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     pages = {33-40},
     doi = {10.5802/acirm.31},
     language = {en},
     url = {acirm.centre-mersenne.org/item/ACIRM_2010__2_2_33_0/}
}
Johnson, Keith. Computing $r$-removed $P$-orderings and $P$-orderings of order $h$. Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 33-40. doi : 10.5802/acirm.31. https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_33_0/

[1] D. Barsky Fonctions k-lipschitziennes sur un anneau local et polynômes à valeurs entières, Bull. Soc. Math. France, Tome 101 (1973), pp. 397-411

[2] M. Bhargava; P.-J. Cahen; J. Yeramian Finite Generation Properties for Various Rings of Integer Valued Polynomials , J. Algebra, Tome 322 (2009), pp. 1129-1150

[3] M. Bhargava The factorial function and generalizations, Am. Math. Monthly, Tome 107 (2000), pp. 783-799

[4] M. Bhargava On P-orderings, Rings of Integer Valued Polynomials and Ultrametric Analysis, J. Amer. Math. Soc., Tome 22(4) (2009), pp. 963-993

[5] M. Bhargava P-orderings and polynomial functions on arbitrary subsets of Dedekind rings, J. Reine Angew. Math., Tome 490 (1997), pp. 101-127

[6] L. Carlitz A Note on Integral Valued Polynomials, Indagationes Math., Ser. A, Tome 62 (1959), pp. 294-299

[7] P.-J. Cahen; J.-L. Chabert Integer Valued Polynomials, Amer. Math. Soc., 1997

[8] K. Johnson P-orderings of Finite Subsets of Dedekind Domains, J. Algebraic Combinatorics, Tome 30 (2009), pp. 233-253

[9] K. Johnson Limits of characteristic sequences of integer-valued polynomials on homogeneous sets, J. Number Theory, Tome 129 (2009), pp. 2933-2942