Publications (19)
Derivation degree sequences of non-free arrangements
Max Wakefield
In this note we study the logarithmic derivation module of a non-free arrangement. We prove a generalized addition theorem for all arrangements. This addition theorem allows us to…
A componentwise version of Terao's conjecture
William N. Traves, Max Wakefield
This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.
Chain characteristic polynomials of matroids
Gary Lazzaro, Max Wakefield, Jason Weiss
In this note we introduce a family of polynomials on a matroid derived from chain Tutte polynomials which generalize the classic and ubiquitous characteristic polynomial. We show t…
Free Multiplicities on the moduli of
Michael DiPasquale, Max Wakefield
In this note we study the freeness of the module of derivations on all moduli of the arrangement with multiplicities. We use homological techniques stemming from work of Yuzv…
The Jacobian ideal of a hyperplane arrangement
Max Wakefield, Masahiko Yoshinaga
The Jacobian ideal of a hyperplane arrangement is an ideal in the polynomial ring whose generators are the partial derivatives of the arrangements defining polynomial. In this arti…
The Kazhdan-Lusztig polynomial of a matroid
Ben Elias, Nicholas Proudfoot, Max Wakefield
We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M, in analogy with Kazhdan-Lusztig polynomials in representa…
Partial flag incidence algebras
Max Wakefield
The partial flag incidence algebra of a poset is the set of functions from to some ring which are zero on non-partial flag vectors. These partial flag incidence…
Derivations of an effective divisor on the complex projective line
Max Wakefield, Sergey Yuzvinsky
In this paper we consider an effective divisor on the complex projective line and associate with it the module D consisting of all the derivations such that $θ(I_i)\subset I_…
Chain Tutte polynomials
Max Wakefield
The Tutte polynomial and Derksen's -invariant are the universal deletion-contraction and valuative matroid and polymatroid invariants, respectively. There are only a h…
Limits with braid arrangements
Matthew S. Miller, Max Wakefield
We define a monoid structure on the set of -equal arrangements and use this structure to define limits of braid arrangements. We compute the cohomology of the associated limits…
A non-associative incidence near-ring with a generalized Möbius function
John Johnson, Max Wakefield
There is a convolution product on 3-variable partial flag functions of a locally finite poset that produces a generalized Möbius function. Under the product this generalized Möbi…
The characteristic polynomial of a multiarrangement
Takuro Abe, Hiroaki Terao, Max Wakefield
Given a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial…
Edge colored hypergraphic arrangements
Matthew Miller, Max Wakefield
A subspace arrangement defined by intersections of hyperplanes of the braid arrangement can be encoded by an edge colored hypergraph. It turns out that the characteristic polynomia…
Intersection cohomology of the symmetric reciprocal plane
Nicholas Proudfoot, Max Wakefield, Benjamin Young
We compute the Kazhdan-Lusztig polynomial of the uniform matroid of rank n-1 on n elements by proving that the i-th coefficient of is equal to the number of ways to choose i non-in…
Skeleton Simplicial Evaluation Codes
James Berg, Max Wakefield
For a subspace arrangement over a finite field we study the evaluation code defined on the arrangement's set of points. The length of this code is given by the subspace arrangement…
The Enumerative Geometry of Hyperplane Arrangements
Thomas Paul, Will Traves, Max Wakefield
We study enumerative questions on the moduli space of hyperplane arrangements with a given intersection lattice . Mnëv's universality theorem suggests that the…
Equivalence classes of Latin squares and nets in CP^2
Corey Dunn, Matthew S. Miller, Max Wakefield +1
The fundamental combinatorial structure of a net in CP^2 is its associated set of mutually orthogonal latin squares. We define equivalence classes of sets of orthogonal Latin squar…
Local cohomology of logarithmic forms
Graham Denham, Hal Schenck, Mathias Schulze +2
Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y, homological invariants derived from logarithmic differential forms alon…
The Euler multiplicity and addition-deletion theorems for multiarrangements
Takuro Abe, Hiroaki Terao, Max Wakefield
The addition-deletion theorems for hyperplane arrangements, which were originally shown in [H. Terao, Arrangements of hyperplanes and their freeness I, II. J. Fac. Sci. Univ. Tokyo…