Computing r -removed P -orderings and P -orderings of order h

Keith Johnson[1]

  • [1] Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 2, page 33-40
  • ISSN: 2105-0597

Abstract

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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 = and S = p .

How to cite

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Johnson, Keith. "Computing $r$-removed $P$-orderings and $P$-orderings of order $h$." Actes des rencontres du CIRM 2.2 (2010): 33-40. <http://eudml.org/doc/196277>.

@article{Johnson2010,
abstract = {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 $S=\mathbb\{Z\}$ and $S=\mathbb\{Z\}\backslash p\mathbb\{Z\}$.},
affiliation = {Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada},
author = {Johnson, Keith},
journal = {Actes des rencontres du CIRM},
keywords = {integer valued polynomials; $p$-orderings; $p$-sequence; divided differences; finite differences},
language = {eng},
number = {2},
pages = {33-40},
publisher = {CIRM},
title = {Computing $r$-removed $P$-orderings and $P$-orderings of order $h$},
url = {http://eudml.org/doc/196277},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Johnson, Keith
TI - Computing $r$-removed $P$-orderings and $P$-orderings of order $h$
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 33
EP - 40
AB - 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 $S=\mathbb{Z}$ and $S=\mathbb{Z}\backslash p\mathbb{Z}$.
LA - eng
KW - integer valued polynomials; $p$-orderings; $p$-sequence; divided differences; finite differences
UR - http://eudml.org/doc/196277
ER -

References

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  2. M. Bhargava, P.-J. Cahen, J. Yeramian, Finite Generation Properties for Various Rings of Integer Valued Polynomials , J. Algebra 322 (2009), 1129-1150 Zbl1177.13051MR2537676
  3. M. Bhargava, The factorial function and generalizations, Am. Math. Monthly 107 (2000), 783-799 Zbl0987.05003MR1792411
  4. M. Bhargava, On P -orderings, Rings of Integer Valued Polynomials and Ultrametric Analysis, J. Amer. Math. Soc. 22(4) (2009), 963-993 Zbl1219.11047MR2525777
  5. M. Bhargava, P -orderings and polynomial functions on arbitrary subsets of Dedekind rings, J. Reine Angew. Math. 490 (1997), 101-127 Zbl0899.13022MR1468927
  6. L. Carlitz, A Note on Integral Valued Polynomials, Indagationes Math., Ser. A 62 (1959), 294-299 Zbl0100.27102MR108462
  7. P.-J. Cahen, J.-L. Chabert, Integer Valued Polynomials, (1997), Amer. Math. Soc. Zbl0884.13010MR1421321
  8. K. Johnson, P -orderings of Finite Subsets of Dedekind Domains, J. Algebraic Combinatorics 30 (2009), 233-253 Zbl1180.13024MR2525060
  9. K. Johnson, Limits of characteristic sequences of integer-valued polynomials on homogeneous sets, J. Number Theory 129 (2009), 2933-2942 Zbl1233.11030MR2560844

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