Papers and
Talk Slides of Paul Renteln
Preprints
- ``Counting Sylow double cosets in
the symmetric group'', October 2023 pdf,
submitted.
Publications
- ``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
Unpublished Manuscripts
- ``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