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Full-Text Articles in Physical Sciences and Mathematics
Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr
Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr
Faculty Publications
Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new …
A Generalized Molien Function For Field Theoretical Hamiltonians, Jeffrey W. Felix, Dorian M. Hatch
A Generalized Molien Function For Field Theoretical Hamiltonians, Jeffrey W. Felix, Dorian M. Hatch
Faculty Publications
A generating function, or Molien function, the coefficients of which give the number of independent polynomial invariants in G, has been useful in the Landau and renormalization group theories of phase transitions. Here a generalized Molien function for a field theoretical Hamiltonian (with short-range interactions) of the most general form invariant in a group G is derived. This form is useful for more general renormalization group calculations. Its Taylor series is calculated to low order for the FGamma-2 representation of the space group R[3 bar]c and also for the l=1 (faithful) representation of SO(3).