Special Rim Hook Tabloids and Some New Multiplicity-Free <i>S</i>-Series

Remmel, J. B.

doi:10.1137/0404024

Cited by 8 publications

(2 citation statements)

References 13 publications

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“…However, their argument (specialize the Cauchy identity for Schur functions), if carefully completed, would also give a proof of (9.10), after some work. It should also be remarked, that by a general theorem of Remmel and Yang [38,Theorem 3.1], the expansion (9.9) (and hence also (9.10)) is multiplicity-free. It should be noted that (9.10) is related to a special case of (3.5) with a horizontal shift S. More precisely, in Proposition 1 take u i = (i, 1), v i = (λ i + i, ∞), i = 1, 2, .…”

Section: Theorem 31 For the Generating Function Of All Linear Partitmentioning

confidence: 98%

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1997

Trans. Amer. Math. Soc.

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A new object is introduced into the theory of partitions that generalizes plane partitions: cylindric partitions. We obtain the generating function for cylindric partitions of a given shape that satisfy certain row bounds as a sum of determinants of q-binomial coefficients. In some special cases these determinants can be evaluated. Extending an idea of Burge (J. Combin. Theory Ser. A 63 (1993), 210-222), we count cylindric partitions in two different ways to obtain several known and new summation and transformation formulas for basic hypergeometric series for the affine root system Ar. In particular, we provide new and elementary proofs for two Ar basic hypergeometric summation formulas of Milne (Discrete Math. 99 (1992), 199-246).

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Section: Theorem 31 For the Generating Function Of All Linear Partitmentioning

confidence: 98%

Untitled

1997

Trans. Amer. Math. Soc.

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“…For instance, Jeff provided a particularly nice combinatorial interpretation for the entries in the inverse Kostka matrix [18,83]. A special rim hook is a sequence of connected cells in the Young diagram of an integer partition (following Jeff's lead, we use the French convention when drawing Young diagrams) that begins in the top left cell and travels along the northeast edge such that its removal leaves the Young diagram of a smaller integer partition.…”

Section: Symmetric Functionsmentioning

confidence: 99%