Publications

• ``Counting Sylow double cosets in the symmetric group'', Discrete Mathematics, 347(10), 2024, 114109 (doi); journal version; preprint version.
  
• ``A natural idempotent in the descent algebra of a finite Coxeter group'', Algebraic Combinatorics, 6(5) (2023), 1177-1188, journal link.
• ``A combinatorial proof of a symmetric group character involution'', pdf (The Version of Record of this manuscript has been published and is available in The American Mathematical Monthly 14 Aug 2023  here).  Also available here journal link (free to the first 50 lucky winners;  one click per customer please)
• ``On the Spectra of Simplicial Rook Graphs'', Graphs and Combinatorics 39(5) (2023) #95, pdf journal link
• ``On the Spectrum of the Perfect Matching Derangement Graph'', Journal of Algebraic Combinatorics (2022), pdf journal link
  
• ``Some Constraints on the Missing Moore Graph'', Australasian Journal of Combinatorics, 77(3) (2020) 373-382. journal link.  Corrigendum: ``On the paper `Some Constraints on the Missing Moore Graph'", Australasian Journal of Combinatorics, 79(1) (2021) 193-194.  journal link.
  
• ``The Distance Spectra of Cayley Graphs of Coxeter Groups'', Discrete Mathematics, 311 (2011) 738-755. pdf journal link
• ``On the Spectrum of the Derangement Graph'', Electronic Journal of Combinatorics, 14(1) (2007), #R82. pdf journal link
• ``Foolproof: A Sampling of Mathematical Folk Humor" (with A. Dundes), Notices of the AMS, 52 (2005) 24-34. pdf
• ``On the Chromatic Number of the Complement of a Class of Line Graphs", Ars Combinatoria, 67 (2003) 33-36.  pdf   ps.gz (note)
• ``The Hilbert Series of the Face Ring of a Flag Complex'', Graphs and Combinatorics, 18 (2002) 3, 605-619.  Journal link here.  Preprint available in pdf.
• Review of Three Roads to Quantum Gravity by Lee Smolin, in American Scientist, 90 (2002) 76-78.  Available here.
• ``Geometric Approaches to the Enumeration of Posets:  An Introductory Survey'', Nieuw Archief voor Wiskunde, 14 (1996) 349-371.
• Review of Black Holes and Time Warps:  Einstein's Outrageous Legacy by Kip Thorne, in American Scientist, 83 (1995) 373-374.
• ``On the Enumeration of Finite Topologies'', Journal of Combinatorics, Information, and System Sciences, 19 (1994) 201-206.
• ``Unification of Forces in Physics'', Encyclopaedia Americana, 1993-2010 Editions, (Grolier Incorporated, Danbury, CT, 1993).
• ``Quantum Gravity'', American Scientist, 79 (1991) 508-527.
• ``Metric Space as a Model of Spacetime:  Classical Theory and Quantization'' (with C.J. Isham and Y. Kubyshin), in The Physical Universe: The Interface Between Cosmology, Astrophysics, and Particle Physics.  Proceedings of the XII Autumn School of Physics (Lisbon, 1-5 October, 1990).  Ed. by J.D. Barrow, A.B. Henriques, M.T.V.T. Lago, and M.S. Longair.  Lecture Notes in Physics, Vol. 383 (Springer-Verlag, Berlin, 1991), pp. 159-173.
• ``Quantum Metric Topology'' (with C.J. Isham and Y. Kubyshin), in Quantum Gravity.  Proceedings of the 5th Seminar (Moscow, 28 May - 1 June 1990).  Ed. by M.A. Markov, V.A. Berezin, and V.P. Frolov.  (World Scientific, Singapore, 1991), pp. 60-82.
• ``Quantum Norm Theory and the Quantization of Metric Topology'' (with C.J. Isham and Y. Kubyshin), Classical and Quantum Gravity, 7, 1990, 1053-1074.
• ``Some Results of SU(2) Spinorial Lattice Gravity'', Classical and Quantum Gravity, 7, 1990, 493-502.
• ``Midrapidity π-/π+ Ratios in 1.05 GeV/nucleon ⁴⁰Ca+⁴⁰Ca Collisions'' (with J.W. Harris, J. Miller, H.G. Pugh, G. Roche, L.S. Schroeder, R.N. Treuhaft, P.N. Kirk, G. Krebs, R. Brockmann, and K.L. Wolf), Physical Review C , 41, 1990, 147-151.
• ``A Lattice Approach to Spinorial Quantum Gravity'' (with L. Smolin), Classical and Quantum Gravity, 6, 1989, 275-294.
• ``A New Lattice Regularization for Quantum Gravity'' in A. Ashtekar (Ed.), New Perspectives in Canonical Gravity (Bibliopoulis, Naples, 1988) Chapter 7, pp. 267-273.

Talk Slides

• An Introduction to Hyperplane Arrangements
• The Spectrum of the Derangement Graph
• The Distance Spectra of Cayley Graphs of Coxeter Groups (Note: See the published article for a proof of the conjecture regarding the eigenvalues of the weak order graphs of types A, D, and E)
• Some Reflection Group Numerology (Note:  An argument due to Matt Fayers shows that the analogue of the normal form theorem fails in types D_n (n>3) and H_3, and is likely to be false for all the other types.)
  

Unpublished Manuscripts
 

• ``Sylow permutation characters in the symmetric group'', December 2024, pdf.
• ``On the spectra of abelian rook graphs'', September 2022, pdf.
• ``Kronecker Coefficients for Three Hook Shapes'', February 2022, pdf.  (The referee felt that the results obtained here were not sufficiently different from those in the existing literature.)
  
• ``A Major Index Determinant'', August 2021, pdf.  (After submitting this paper for publication I was informed by the referee that a similar result (using similar methods) had been obtained six months earlier by T. Mcconville, D. Robertson, and C. Smyth (Determinantal formulas with major Indices, arXiv:2102.13005).  My proof is a bit quicker, but theirs is more comprehensive, as they obtain various extensions of the result.  (For a proof of Theorem 1 in my paper they reference a paper of R. Adin and Y. Roichman (The flag major index and group actions on polynomials rings, Eur. J. Combin., 22(4), 2001, 431-446).))
• ``Totally Symmetric Equiangular Line Sets'', August 2016, pdf.
  
• ``A Bound on the Number of Minimum Covers of a Hypergraph'', August, 2003,  pdf