On the interconnectedness of things

Like much of the discrete math community, my Erdos number is 2, via, for example

  1. P. Erdos and P. Tetali, Representations of integers as the sum of k terms
    Random Structures and Algorithms 1 (1990), 245--261.
  2. D. Galvin and P. Tetali, On weighted graph homomorphisms
    in Graphs, Morphisms and Statistical Physics,
    DIMACS series in discrete mathematics and theoretical computer science, J. Nestril and P. Winkler eds (2004).

This pleases me. It pleases me as much that there are paths through the collaboration graph linking me with many good friends and colleagues around the globe. I present here some of these. The usual caveat of the pure mathematician applies: no attempt has been made to optimize the constants!

The honour roll of those appearing on this list:

A path to Martin Christlieb

Martin is a researcher at the Gray Institute, University of Oxford.

  1. D. Radnell and E. Schippers, Quasisymmetric sewing in rigged Teichmueller space
    Communications in Contemporary Mathematics 8 (2006), 481-534.
  2. O. Roth and E. Schippers, The Loewner and Hadamard variations
    Illinois Journal of Mathematics.
  3. D. Kraus, O. Roth and S. Ruscheweyh, A boundary version of Ahlfors' lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps
    Journal d'Analyse Mathematique 101 (2007), 219--256.
  4. R. Hall and S. Ruscheweyh, On transforms of functions with bounded boundary rotation
    Indian Journal of Pure and Applied Mathematics 16 (1985), 1317--1325.
  5. P. Erdos and R. Hall, On the values of Euler's phi function
    Acta Arithmetica 22 (1973), 201--206.
  6. P. Erdos and P. Tetali, Representations of integers as the sum of k terms
    Random Structures and Algorithms 1 (1990), 245--261.
  7. D. Galvin and P. Tetali, On weighted graph homomorphisms
    in Graphs, Morphisms and Statistical Physics,
    DIMACS series in discrete mathematics and theoretical computer science, J. Nestril and P. Winkler eds (2004).

A path to Kia Dalili

Kia is an AARMS Postdoctoral Fellow working at Dalhousie university in Halifax, Nova Scotia.

  1. K. Dalili and W. Vasconcelos, The tracking number of an algebra
    Amer. J. Math 127 (2005) 697-708.
  2. D. Eisenbud, W. Vasconcelos and R. Wiegand, Projective summands in generators
    Nagoya Math. J. 86 (1982) 203-209.
  3. J. Buhler, D. Eisenbud, R. Graham, and C. Wright, Juggling drops and descents
    Amer. Math. Monthly 101 (1994) 507-519.
  4. G. Brightwell and C. Wright, The 1/3-2/3 conjecture for 5-thin posets
    SIAM J. Discrete Math. 5 (1992) 467-474.
  5. G. Brightwell, P. Tetali, The number of linear extensions of the Boolean lattice
    Order 20 (2003) 333-345.
  6. D. Galvin and P. Tetali, On weighted graph homomorphisms
    in Graphs, Morphisms and Statistical Physics,
    DIMACS series in discrete mathematics and theoretical computer science, J. Nestril and P. Winkler eds (2004)

A path to John Huber

John is a lecturer in Engineering Science and a fellow of Oriel College, Oxford.

  1. J. Huber and N. Fleck, Ferroelectric switching: a micromechanics model versus measured behaviour
    European Journal of Mechanics A/Solids 23 (2004), 203-217.
  2. N. Fleck and J. Hutchinson, A phenomenological theory for strain gradient plasticity
    J. Mech. Phys. Solids 41 (1993), 1825-1857.
  3. J. Hutchinson and F. Niordson, Designing Vibrating Membranes
    in Continuum Mechanics and Related Problems of Analysis, Nauka Publishing House, Moscow, 1972, pp. 581-590.
  4. J. Keller and F. Niordson, The Tallest Column
    J. Math. Mech. 16 (1966) 433-446.
  5. P. Diaconis and J. Keller, Fair Dice
    Am. Math. Monthly 96 (1989), 337-339.
  6. F. Chung, P. Diaconis and R. Graham, Random walks arising in random number generation
    Ann. Prob.     15 (1986), 1148-1165.
  7. F. Chung and P. Tetali, Isoperimetric inequalities for Cartesian products of graphs
    Combinatorics, Probability and Computing 7 (1998), 141-148
  8. David Galvin and Prasad Tetali, On weighted graph homomorphisms
    in Graphs, Morphisms and Statistical Physics,
    DIMACS series in discrete mathematics and theoretical computer science, J. Nestril and P. Winkler eds (2004)

A path to Andrew Lovatt

  1. A. Lovatt and H. Shercliff, Manufacturing process selection in engineering design. Part 1: the role of process selection
    Materials and Design 19 (1998), 205-215.
  2. N. Fleck and H. Shercliff, Effect of specimen geometry on fatigue crack-growth in plane-strain Part 2: Overload response
    Fatigue & Fracture of Engineering Materials & Structures 13 (1990), 297-310.
  3. N. Fleck and J. Hutchinson, A phenomenological theory for strain gradient plasticity
    J. Mech. Phys. Solids 41 (1993), 1825-1857.
  4. J. Hutchinson and F. Niordson, Designing Vibrating Membranes
    in Continuum Mechanics and Related Problems of Analysis, Nauka Publishing House, Moscow, 1972, pp. 581-590.
  5. J. Keller and F. Niordson, The Tallest Column
    J. Math. Mech. 16 (1966) 433-446.
  6. P. Diaconis and J. Keller, Fair Dice
    Am. Math. Monthly 96 (1989), 337-339.
  7. F. Chung, P. Diaconis and R. Graham, Random walks arising in random number generation
    Ann. Prob.     15 (1986) 1148-1165.
  8. F. Chung and P. Tetali, Isoperimetric inequalities for Cartesian products of graphs
    Combinatorics, Probability and Computing 7 (1998), 141-148
  9. David Galvin and Prasad Tetali, On weighted graph homomorphisms
    in Graphs, Morphisms and Statistical Physics,
    DIMACS series in discrete mathematics and theoretical computer science, J. Nestril and P. Winkler eds (2004)

A path to Antun Milas

Antun is at the Department of Mathematics and Statistics at the University of Albany.

  1. B. Doyon, J. Lepowsky and A. Milas, Twisted modules for vertex operator algebras and Bernoulli polynomials
    Int. Math. Res. Not. (2003), 2391-2408.
  2. J. Lepowsky and S. Milne, Lie algebras and classical partition identities
    Proc. Nat. Acad. Sci. U.S.A. 75 (1978), 578-579.
  3. L. Biedenharn, W. Holman and S. Milne, The invariant polynomials characterizing U(n) tensor operators (p,q,...,q,0,...0) having maximal null space
    Adv. in Appl. Math. 1 (1980) 390-472.
  4. L. Biedenharn, W. Chen, M. Lohe and J. Louck, The role of SU(2) 3n-j coefficients in SU(3)
    Symmetry and structural properties of condensed matter (Zajpolhk aczkowo, 1994), 150--182.
    (World Sci. Publishing, River Edge, NJ, 1995).
  5. W. Chen and J. Kung, The combinatorics of symmetric functions. Gian-Carlo Rota on combinatorics, 458--467.
    (Contemp. Mathematicians, Birkhäuser Boston, Boston, MA, 1995).
  6. J. Kahn and J. Kung, Varieties and universal models in the theory of combinatorial geometries
    Bull. Amer. Math. Soc. (N.S.) 3 (1980) 857-858.
  7. D. Galvin and J. Kahn, On phase transition in the hard-core model on Z^d
    Combinatorics, Probability and Computing 13 (2004) 137-164.

A path to Assaf Naor

Assaf is a reseacher in the Theory Group at Microsoft Reseach.

  1. E. Friedgut, G. Kalai and A. Naor, Boolean Functions whose Fourier Transform is Concentrated on the First Two Levels
    Advances in Applied Mathematics 29 (2002) 427-437.
  2. E. Friedgut and J. Kahn, On the Number of Copies of One Hypergraph in Another
    Israel Journal of Mathematics 105 (1998) 251-256.
  3. D. Galvin and J. Kahn, On phase transition in the hard-core model on Z^d
    Combinatorics, Probability and Computing 13 (2004) 137-164.

A path to Clifford Smyth

Cliff is an Instructor in Applied Mathematics at MIT.

  1. J. Kahn, M. Saks and C. Smyth, A dual version of Reimer's inequality and a proof of Rudich's conjecture
    15th Annual IEEE Conference on Computational Complexity (Florence, 2000) 98--103.
  2. D. Galvin and J. Kahn, On phase transition in the hard-core model on Z^d
    Combinatorics, Probability and Computing 13 (2004) 137-164.

A path to James Taylor

  1. S. Goldstein, J. Taylor, R. Tumulka and N. Zanghi, Are all particles identical?
    J. Phys. A 38 (2005) 1567-1576.
  2. S. Goldstein, R. Kuik, J. Lebowitz and C. Maes, From PCAs to equilibrium systems and back
    Comm. Math. Phys. 125 (1989) 71-79.
  3. J. van den Berg and C. Maes, Disagreement percolation in the study of Markov fields
    Ann. Probab. 22 (1994) 749-763.
  4. J. van den Berg and J. Kahn, A correlation inequality for connection events in percolation
    Ann. Probab. 29 (2001) 123--126.
  5. D. Galvin and J. Kahn, On phase transition in the hard-core model on Z^d
    Combinatorics, Probability and Computing 13 (2004) 137-164.

A path to David Radnell

David is an Assistant Professor at the American University in Sharjah.

  1. D. Radnell and E. Schippers, Quasisymmetric sewing in rigged Teichmueller space
    Communications in Contemporary Mathematics 8 (2006), 481-534.
  2. O. Roth and E. Schippers, The Loewner and Hadamard variations
    Illinois Journal of Mathematics.
  3. D. Kraus, O. Roth and S. Ruscheweyh, A boundary version of Ahlfors' lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps
    Journal d'Analyse Mathematique 101 (2007), 219--256.
  4. R. Hall and S. Ruscheweyh, On transforms of functions with bounded boundary rotation
    Indian Journal of Pure and Applied Mathematics 16 (1985), 1317--1325.
  5. P. Erdos and R. Hall, On the values of Euler's phi function
    Acta Arithmetica 22 (1973), 201--206.
  6. P. Erdos and P. Tetali, Representations of integers as the sum of k terms
    Random Structures and Algorithms 1 (1990), 245--261.
  7. D. Galvin and P. Tetali, On weighted graph homomorphisms
    in Graphs, Morphisms and Statistical Physics,
    DIMACS series in discrete mathematics and theoretical computer science, J. Nestril and P. Winkler eds (2004).

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