Publications

Art Duval

Slides from (recent) talks

(full-color slideshows)

Enumerating simplicial spanning trees of shifted and color-shifted complexes, using simplicial effective resistance.: Algebra seminar, New Mexico State University (online). February 28, 2022.; .pdf
Enumerating simplicial spanning trees of shifted and color-shifted complexes, using simplicial effective resistance.: AMS Central Sectional Meeting, online (formerly University of Creighton), October 9, 2021.; .pdf
Counting topologies of holomorphic polynomial fields with simple zeros: 31 Semana Nacional de Investigación y Docencia en Matematicás, Universidad de Sonora, May 27, 2021.; .pdf
What is 0⁰, and who decides, and why does it matter?: The role of definitions in mathematics: STEMERS (STEM Education Research Seminar), Dept. of Teacher Education, UTEP (online). November 13, 2020.; .pdf
A non-partitionable Cohen-Macaulay simplicial complex: 30 Semana Nacional de Investigación y Docencia en Matematicás, Universidad de Sonora, March 2, 2020.; .pdf
All talks, back to 2003.

A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes: (w/Ghodratollah Aalipour, Univ. of Colorado Denver, Woong Kook, Seoul National University, Kang-Ju Lee, Seoul National University and Jeremy Martin, Univ. of Kansas); Journal of Combinatorial Theory (Series A) 158 (2018), 362-386.; ScienceDirect link to abstract and .pdf
The partitionability conjecture: (w/Caroline (Carly) Klivans, Brown Univ. and Jeremy Martin, Univ. of Kansas); Notices of the American Mathematical Society 64 (2017), 117-122.; article in .pdf
A non-partitionable Cohen-Macaulay simplicial complex: (w/Bennet Goeckner, Univ. of Kansas, Caroline (Carly) Klivans, Brown Univ. and Jeremy Martin, Univ. of Kansas); Advances in Mathematics 299 (2016), 381-395.; ScienceDirect link to abstract and .pdf
Simplicial and cellular trees: (w/Caroline (Carly) Klivans, Brown Univ. and Jeremy Martin, Univ. of Kansas); in "Recent Trends in Combinatorics", IMA Volumes in Mathematics and its Applications 159 (Springer, 2016), pp. 713-752;; SpringerLink to abstract and article; preprint arXiv:1506.06819 [math.CO] (abstract, link to .pdf)
Cuts and flows of cell complexes: (w/Caroline (Carly) Klivans, Brown Univ. and Jeremy Martin, Univ. of Kansas); Journal of Algebraic Combinatorics 41 (2015), 969-999.; SpringerLink to online abstract and .pdf
Critical groups of simplicial complexes: (w/Caroline (Carly) Klivans, Brown Univ. and Jeremy Martin, Univ. of Kansas); Annals of Combinatorics 17 (2013), 53-70.; SpringerLink to abstract and .pdf
Algorithms to determine the edges of a convex hull from its vertices: (w/Francisco J. Lopez, Macon State College); International Journal Mathematical Modelling and Numerical Optimisation 3 (2012), 184-209.; Inderscience link to .pdf
Cellular spanning trees and Laplacians of cubical complexes: (w/Caroline (Carly) Klivans, Brown Univ. and Jeremy Martin, Univ. of Kansas); Advances in Appplied Mathematics 46 (2011), 247-274.; ScienceDirect link to pdf.
Simplicial matrix-tree theorems: (w/Caroline (Carly) Klivans, Brown Univ. and Jeremy Martin, Univ. of Kansas); Transactions of the American Mathematical Society 361 (2009), 6073-6114.; abstract, references, .pdf
A Relative Laplacian Spectral Recursion: Electronic Journal of Combinatorics 11(2) (2006) , R26, 19pp.; abstract, .ps, .pdf,
A Common Recursion for Laplacians of Matroids and Shifted Simplicial Complexes: Documenta Mathematica 10 (2005), 583-618.; abstract, .dvi.gz, .dvi, .ps.gz, .pdf.
Semidirect Product Constructions of Directed Strongly Regular Graphs: (w/Dmitri Iourinski, my former M.S. student); Journal of Combinatorial Theory (Series A) 104 (2003), 157-167.; abstract, full-text.
Shifted Simplicial Complexes are Laplacian Integral: (w/Vic Reiner, Univ. of Minnesota); Transactions of the American Mathematical Society 354 (2002), 4313-4344.; abstract,.tex,.dvi,.ps,.pdf,references
Algebraic Shifting and Spectral Sequences: Advanced Studies in Pure Mathematics 33 (2002), Computational Commutative Algebra and Combinatorics, pp. 53-64.; abstract.
Iterated Homology and Decompositions of Simplicial Complexes: (w/Ping Zhang, Western Michigan Univ.); Israel Journal of Mathematics 121 (2001), 313-331.; abstract, SpringerLink to .pdf.
Iterated Homology of Simplicial Complexes: (w/Lauren Rose, Bard College),; Journal of Algebraic Combinatorics 12 (2000), 279-294.; abstract, SpringerLink to .pdf.
Algebraic Shifting Increases Relative Homology,: Discrete Mathematics 225 (2000), 137-148.; abstract, ScienceDirect link to .pdf.
Perron-Frobenius Type Results and Discrete Versions of Nodal Domain Theorems: (w/Vic Reiner, Univ. of Minnesota),; Linear Algebra and its Applications 294 (1999), 259-268.; abstract, ScienceDirect link to .pdf.
On f-vectors and Relative Homology,: Journal of Algebraic Combinatorics 9 (1999), 215-232.; abstract, SpringerLink to .pdf.
Free Resolutions of Simplicial Posets,: Journal of Algebra 188 (1997), 363-399.; abstract, ScienceDirect link to .pdf.
Algebraic Shifting and Sequentially Cohen-Macaulay Simplicial Complexes,: Electronic Journal of Combinatorics 3 (1996), R21, 14pp.; abstract,.tex,.dvi,.ps,.pdf
Covering a Circular String with Substrings of Fixed Length: (w/ Bill Smyth, McMaster Univ. and Curtin Univ.),; International Journal of Foundations of Computer Science 7 (1996), 87-93.; abstract, WorldScientific link to .pdf.
Orderpotent f-rings: (w/Piotr Wojciechowski, UTEP),; Algebra Universalis 34 (1995), 510-526.; abstract , SpringerLink to .pdf.
A Combinatorial Decomposition of Simplicial Complexes,: Israel Journal of Mathematics 87 (1994), 77-87.; abstract, SpringerLink to .pdf.
A Directed Graph Version of Strongly Regular Graphs,: Journal of Combinatorial Theory (Series A) 47 (1988), 71-100.; abstract , ScienceDirect link to .pdf.