The Umbral Calculus of Symmetric Functions

Méndez, Miguel

doi:10.1006/aima.1996.0083

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…But the chromatic polynomial is a polynomial, so it must be true in general. ✷ For the chromatic polynomial, (10) and (12) give the following expansions.…”

Section: Theorem 16mentioning

confidence: 99%

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Set maps, umbral calculus, and the chromatic polynomial

Wiseman

2008

Discrete Mathematics

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“…But the chromatic polynomial is a polynomial, so it must be true in general. ✷ For the chromatic polynomial, (10) and (12) give the following expansions.…”

Section: Theorem 16mentioning

confidence: 99%

“…Further generality can be obtained by replacing K[x] by a different coalgebra. For example, Méndez's umbral calculus of symmetric functions [12] can be used to generalize the results of Section 6 to Stanley's chromatic symmetric function [19].…”

Section: Notesmentioning

confidence: 99%

Set maps, umbral calculus, and the chromatic polynomial

Wiseman

2008

Discrete Mathematics

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“…Rota's pioneer work was completed in the next decade by Rota and his collaborators [13,14,17]. Since then, there have been a number of generalizations of the umbral calculus [4,9,10,13,18].…”

Section: Introductionmentioning

confidence: 98%

Baxter Algebras and the Umbral Calculus

Guo

2001

Advances in Applied Mathematics

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dedicated to dominique foata on his 65th birthdayWe apply recent constructions of free Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of the Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that includes the classical umbral calculus in a family of λ-umbral calculi parameterized by λ in the base ring.  2001 Elsevier Science

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“…, m − 1}. M. Mendez [29,30] developed an umbral calculus for symmetric functions including the factorial Schur function and the double Schur function. Molev and Sagan [32] have recently obtained the Littlewood-Richardson rule for the factorial Schur function.…”

Section: Introductionmentioning

confidence: 99%

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Chen

Louck

2002

Journal of Algebraic Combinatorics

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Abstract. The double Schur function is a natural generalization of the factorial Schur function introduced byBiedenharn and Louck. It also arises as the symmetric double Schubert polynomial corresponding to a class of permutations called Grassmannian permutations introduced by A. Lascoux. We present a lattice path interpretation of the double Schur function based on a flagged determinantal definition, which readily leads to a tableau interpretation similar to the original tableau definition of the factorial Schur function. The main result of this paper is a combinatorial treatment of the flagged double Schur function in terms of the lattice path interpretations of divided difference operators. Finally, we find lattice path representations of formulas for the symplectic and orthogonal characters for sp(2n) and so(2n + 1) based on the tableau representations due to King and El-Shakaway, and Sundaram. Based on the lattice path interpretations, we obtain flagged determinantal formulas for these characters.

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The Umbral Calculus of Symmetric Functions

Cited by 6 publications

References 19 publications

Set maps, umbral calculus, and the chromatic polynomial

Set maps, umbral calculus, and the chromatic polynomial

Baxter Algebras and the Umbral Calculus

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