Disturbing the Dyson conjecture, in a generally GOOD way

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Disturbing the Dyson conjecture, in a generally GOOD way

Dyson’s celebrated constant term conjecture (J. Math. Phys., 3 (1962): 140–156) states that the constant term in the expansion of ∏ 15i6=j5n(1 − xi/xj)j is the multinomial coefficient (a1 +a2 + · · ·+an)!/(a1!a2! · · · an!). The definitive proof was given by I. J. Good (J. Math. Phys., 11 (1970) 1884). Later, Andrews extended Dyson’s conjecture to a q-analog (The Theory and Application of Speci...

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Disturbing the Dyson Conjecture (in a GOOD Way)

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Abstract. In this paper we study Dyson’s classical r-component hierarchical model with a Hamiltonian function which has a continuous O(r)-symmetry, r ≥ 2.This is a one-dimensional ferromagnetic model with a long range interaction potential U(i, j) = −l(d(i, j))d(i, j), where d(i, j) denotes the hierarchical distance. We are interested in the case when l(t) is a slowly increasing positive functi...

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ژورنال

عنوان ژورنال: Journal of Combinatorial Theory, Series A

سال: 2006

ISSN: 0097-3165

DOI: 10.1016/j.jcta.2005.12.005