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Enumeration	Reference	Cover	Find
1.	Rosengren, Hjalmar, 1972 (author) Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux 2008 In: Journal of Combinatorial Theory A. - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 115:3, s. 376-406 Journal article (peer-reviewed)abstract We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic hypergeometric series, and as determinants and pfaffians of continuous q-ultraspherical or continuous q-Jacobi polynomials. As special cases, we obtain simple closed formulas for staircase-type partitions.
2.	Rosengren, Hjalmar, 1972 (author) Sums of squares from elliptic pfaffians 2008 In: International Journal of Number Theory. ; 4, s. 873-902 Journal article (peer-reviewed)abstract We give a new proof of Milne's formulas for the number of representations of an integer as a sum of 4m^2 and 4m(m+1) squares. The proof is based on explicit evaluation of pfaffians with elliptic function entries, and relates Milne's formulas to Schur Q-polynomials and to correlation functions for continuous dual Hahn polynomials. We also state a new formula for 2m^2 squares.

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University: University of Gothenburg (2); Chalmers University of Technology (2)

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