Combinatory Analysis. Vol. II. By Major P. A. Macmahon. Pp. xix + 340. 18s. net. 1916. (Camb. Univ. Press.)

Mathews, G. B.

doi:10.2307/3605230

Cited by 2 publications

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“…In the work of Percy MacMahon [20] the author illustrates partition analysis by solving combinatorics problems. Suppose we want to find all non-negative integer solutions to 3a − 2b + c = 0.…”

Section: Omega Calculusmentioning

confidence: 99%

“…It can be shown that both the function before applying the operator and the one after are Elliott-rational functions [20]. In the 3a − 2b + c = 0 example eq.…”

Section: Omega Calculusmentioning

confidence: 99%

“…A shortcoming of this strategy is the sometimes insurmountable calculation of a very large number of residues of multivariate integrals. Here, we introduce a technique developed by P. MacMahon [20], later called Omega calculus. With it, many challenging complex integrals become attainable, as we will show with the very complicated case of the 3HDM.…”

Section: Introductionmentioning

confidence: 99%

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The invariant space of multi-Higgs doublet models

Bento

2021

J. High Energ. Phys.

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In a model with more than one scalar doublet, the parameter space encloses both physical and unphysical information. Invariant theory provides a detailed description of the counting and characterization of the physical parameter space. The Hilbert series for the 3HDM is computed for the first time using partition analysis, in particular Omega calculus, giving rise to the possibility of a full description of its physical parameters. A rigorous counting of the physical parameters is given for the full class of models with N scalar doublets as well as a decomposition of the Lagrangian into irreducible representations of SU(N). For the first time we derive a basis-invariant technique for counting parameters in a Lagrangian with both basis-invariant redundancies and global symmetries.

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Section: Omega Calculusmentioning

confidence: 99%

“…It can be shown that both the function before applying the operator and the one after are Elliott-rational functions [20]. In the 3a − 2b + c = 0 example eq.…”

Section: Omega Calculusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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