Published papers

(See also my preprints.)

Citation counts are taken from Google Scholar, which on occasion overcounts slightly.

  1. Robert M. Guralnick, John Shareshian, and Russ Woodroofe, On invariable generation of alternating groups by elements of prime and prime power order. To appear in Math. Comp.
  2. Remark:

    Joni Teräväinen has addressed the question implicitly asked before Section 5.1. He showed in a recent preprint (arXiv:2203.05427) that An is generated by two elements of prime order except possibly on a set of density zero. He gives concrete upper bounds, and does so without use of the Riemann hypothesis.

  3. Russ Woodroofe, An algebraic groups perspective on Erdős-Ko-Rado. To appear in Linear Multilinear Algebra.


    In Lemma 4.3 and the preceding two paragraphs, the indices 1 and 2 are reversed in several places.

  4. Stephan Foldes and Russ Woodroofe, A modular characterization of supersolvable lattices, Proc. Amer. Math. Soc. 150 (2022), no. 1, 31–39.

  5. Andrés Santamaría-Galvis and Russ Woodroofe, Shellings from relative shellings, with an application to NP-completeness, Discrete Comput. Geom. 66 (2021), no. 2, 792–807.


    In Lemma 2.1, the facets of Δa should be facets in the ambient complex (that is, no such facet should be contained in a face of Δb).

  6. John Shareshian and Russ Woodroofe, Divisibility of binomial coefficients and generation of alternating groups, Pacific J. Math. 292 (2018), no. 1, 223–238.

    Attachments: the GAP code discussed in Section 6, together with its output.


    Additional related OEIS entries include: OEIS A290203 and OEIS A290290 (both submitted by Sílvia Casacuberta Puig).

  7. Alireza Abdollahi, Russ Woodroofe, and Gjergji Zaimi, Frankl's Conjecture for subgroup lattices, Electron. J. Combin. 24 (2017), no. 3, Paper 25, 9 pages.

  8. Jay Schweig and Russ Woodroofe, A broad class of shellable lattices, Adv. Math. 313 (2017), 537–563.

  9. John Shareshian and Russ Woodroofe, Order complexes of coset posets of finite groups are not contractible, Adv. Math. 291 (2016), 758–773.

  10. Huy Tài Hà and Russ Woodroofe, Results on the regularity of square-free monomial ideals, Adv. Appl. Math. 58 (2014), 21–36.

    Erratum 1:

    There was an error in our original proof of Lemma 3.4 in the paper, as was pointed out by Fahimeh Khosh-Ahang and Somayeh Moradi in this arXiv preprint. A corrected proof is in the corrigendum published here. (It is also attached at the end of the arXiv version of the paper.) We are grateful to Khosh-Ahang and Moradi for bringing the error to our attention.

    Erratum 2:

    There is an error in the statement of Theorem 5.4 in the paper, as was pointed out by Yusuf Civan: the bound is by the maximum length of an minimal ordered face, where we order the family of ordered faces by σ < τ if σ is an initial substring of τ. A counterexample to the unordered statement may be found by gluing two octahedra together along a common triangle to form a complex G, then gluing an edge from the common triangle of 4 copies of G to each edge of a 4-cycle (considered as a 1-dimensional simplicial complex). We thank Civan for pointing out the problem in the proof, and for help in devising the counterexample.

  11. Russ Woodroofe, Matchings, coverings, and Castelnuovo-Mumford regularity, J. Commut. Algebra 6 (2014), no. 2, 287–304.

  12. Stephan Foldes and Russ Woodroofe, Antichain cutsets of strongly connected posets, Order 30 (2013), no. 2, 351–361.

  13. Russ Woodroofe, Chains of modular elements and shellability, J. Combin. Theory Ser. A 119 (2012), no. 6, 1315–1327.

  14. John Shareshian and Russ Woodroofe, A new subgroup lattice characterization of finite solvable groups, J. Algebra 351 (2012), no. 1, 448–458.

  15. Russ Woodroofe, Chordal and sequentially Cohen-Macaulay clutters, Electron. J. Combin. 18 (2011), no. 1, Paper 208, 20 pages.

    Attachments: the lists of forbidden minors and GAP source referenced in Section 7:
  16. Russ Woodroofe, Erdős-Ko-Rado theorems for simplicial complexes, J. Combin. Theory Ser. A 118 (2011), no. 4, 1218–1227.

  17. Russ Woodroofe, Vertex decomposable graphs and obstructions to shellability, Proc. Amer. Math. Soc. 137 (2009), no. 10, 3235–3246.


    At the end of Section 6, the direct product of two edges is shellable. The direct product of an edge and a 3-cycle is bipartite, and is not shellable or sCM, but is not K3,3. I thank Sara Saeedi for pointing out my mistake.

  18. Russ Woodroofe, Cubical convex ear decompositions, Electron. J. Combin. 16 (2009), no. 2, Research Paper 17, 33 pages.

  19. Russ Woodroofe, An EL-labeling of the subgroup lattice, Proc. Amer. Math. Soc. 136 (2008), no. 11, 3795–3801.

  20. Russ Woodroofe, Shelling the coset poset, J. Combin. Theory Ser. A 114 (2007), no. 4, 733–746.


    The history of shelling in this paper is incomplete: the idea of shellability goes back considerably before Bruggesser and Mani. Even the term shelling goes back at least to Donald Sanderson's 1957 paper Isotopy in 3-Manifolds I. Isotopic Deformations of 2-Cells and 3-Cells. RH Bing discusses shellings at some length in his 1964 book Some aspects of the topology of 3-manifolds related to the Poincaré conjecture.
    Günter Ziegler's paper Shelling Polyhedral 3-Balls and 4-Polytopes has a nice discussion of the history of nonshellable balls.


    A simpler construction of an EL-labeling for the coset lattice of a complemented group is in Section 4.2 of my paper Cubical convex ear decompositions. See above.

  21. Alexander Barvinok, Sándor P. Fekete, David S. Johnson, Arie Tamir, Gerhard J. Woeginger, and Russ Woodroofe, The geometric maximum traveling salesman problem, J. ACM 50 (2003), no. 5, 641–664 (electronic).

  22. Alexander Barvinok, David S. Johnson, Gerhard J. Woeginger, and Russ Woodroofe, The maximum traveling salesman problem under polyhedral norms, Integer programming and combinatorial optimization (Houston, TX, 1998), Lecture Notes in Comput. Sci., vol. 1412, Springer, Berlin, 1998, 195–201.