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This errata sheet is organized by which printing of the book you have. The printing can be found by looking at the string of digits 10 9 8. .. at the bottom of the copyright page: the last digit that appears in this decreasing string indicates the printing.

- John Little, Hal Schenck
- SIAM J. Discrete Math.
- 2006

Toric codes are evaluation codes obtained from an integral convex polytope P ⊂ R n and finite field Fq. They are, in a sense, a natural extension of Reed-Solomon codes, and have been studied recently in [6], [8], [9], and [12]. In this paper, we obtain upper and lower bounds on the minimum distance of a toric code constructed from a polygon P ⊂ R 2 by… (More)

- Leah Gold, John Little, Hal Schenck
- 2003

Hansen (Appl. Algebra Eng. Comm. Comput. 14 (2003) 175) uses cohomological methods to find a lower bound for the minimum distance of an evaluation code determined by a reduced complete intersection in P 2. In this paper, we generalize Hansen's results from P 2 to P m ; we also show that the hypotheses of Hansen (2003) may be weakened. The proof is succinct… (More)

- Klim Efremenko, J. M. Landsberg, Hal Schenck, Jerzy Weyman
- ArXiv
- 2015

The minimal free resolution of the Jacobian ideals of the determinant polynomial were computed by Lascoux [12], and it is an active area of research to understand the Jacobian ideals of the permanent, see e.g., [13, 9]. As a step in this direction we compute several new cases and completely determine the linear strands of the minimal free resolutions of the… (More)

- Brian Harbourne, Hal Schenck, Alexandra Seceleanu
- J. London Math. Society
- 2011

In [19], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x 1 ,. .. , x 4 ] generated by powers of linear forms. This is in contrast to the analogous situation in K[x 1 , x 2 , x 3 ], where WLP always holds [24]. We use the inverse system dictionary to connect I to an ideal of fat points, and show that failure of… (More)

We study the commutative algebra of three bihomogeneous poly-nomials p 0 , p 1 , p 2 of degree (2, 1) in variables x, y; z, w, assuming that they never vanish simultaneously on P 1 ×P 1. Unlike the situation for P 2 , the Koszul complex of the p i is never exact. The purpose of the article is to illustrate how bigraded commutative algebra differs from the… (More)

- Hal Schenck
- Journal of Approximation Theory
- 2014

- Klim Efremenko, J. M. Landsberg, Hal Schenck, Jerzy Weyman
- ArXiv
- 2016

The method of shifted partial derivatives introduced in [9, 7] was used to prove a super-polynomial lower bound on the size of depth four circuits needed to compute the permanent. We show that this method alone cannot prove that the padded permanent ℓ n−m perm m cannot be realized inside the GL n 2-orbit closure of the determinant detn when n > 2m 2 + 2m.… (More)

- Hal Schenck, Alexandra Seceleanu, Javid Validashti
- Math. Comput.
- 2014

Let U ⊆ H 0 (O P 1 ×P 1 (2, 1)) be a basepoint free four-dimensional vector space. The sections corresponding to U determine a regular map φ U : P 1 × P 1 −→ P 3. We study the associated bigraded ideal I U ⊆ k[s, t; u, v] from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free… (More)

- Thomas Bauer, Cristiano Bocci, +11 authors Zach Teitler
- 2012