Erratum to Punctured Combinatorial Nullstellensätze

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corollary_p378: The erratum's replacement for Corollary 4.2 keeps only the lower bounds on the exponents of a forced monomial.

counterexample: Shows that a reduced grid polynomial can contain a monomial absent from the original polynomial.

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Simeon Ball and Oriol Serra, Erratum to: Punctured Combinatorial Nullstellensätze, Combinatorica 31 (2011), no. 3, 377–378, DOI 10.1007/s00493-011-2837-7. The publisher record gives received 16 May 2011, issue date May 2011, and online publication 8 September 2011. These are distinct date fields.

The copy read for this card is the published two-page erratum, printed pp. 377–378. Both pages were checked against the statements recorded here. The erratum prints "©2011 János Bolyai Mathematical Society and Springer-Verlag" on its first page.

What is corrected

The first page restates the original Theorem 4.1. The second page identifies the error in the deduction of Corollary 4.2: a suitable monomial of the normal remainder need not occur in the original polynomial. The published counterexample has a normal remainder proportional to $X_1X_2$, although that monomial does not occur in $f$.

The erratum's replacement corollary (p. 378, unnumbered) retains the coordinate lower bounds $r_i\ge|S_i|-|D_i|$ and removes the upper bounds $r_i\le|S_i|-1$. The corrected statement has one canonical home: Corollary 4.2 in the main source. That page explicitly retains the needed nonzero-on-the-grid hypothesis from Theorem 4.1, which the short printed corollaries leave implicit.

The main source card describes both the corrected nine-page author manuscript dated 14 June 2011 and the older ten-page author manuscript dated 21 January 2009. Neither is presented as the original journal typesetting. The erratum's example is checked in full here. The erratum prints no proof of the corrected corollary. No checked formalization is asserted for this unit.

Bears on

No Erdős problem. The erratum names none, and no problem page cites it.

No file of this source is held: no license on record permits its redistribution, and the card cites the edition it names above.