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Schubert polynomials and $k$-Schur functions (Extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function can be understood from the multiplication in the space of dual $k$-Schur functions. Using earlier work by the second author,
Carolina Benedetti, Nantel Bergeron
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Hall-Littlewood Polynomials in terms of Yamanouchi words [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 This paper uses the theory of dual equivalence graphs to give explicit Schur expansions to several families of symmetric functions. We begin by giving a combinatorial definition of the modified Macdonald polynomials and modified Hall-Littlewood ...
Austin Roberts
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The shifted plactic monoid (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We introduce a shifted analog of the plactic monoid of Lascoux and Schützenberger, the \emphshifted plactic monoid. It can be defined in two different ways: via the \emphshifted Knuth relations, or using Haiman's mixed insertion.
Luis Serrano
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Skew quantum Murnaghan-Nakayama rule [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 In this extended abstract, we extend recent results of Assaf and McNamara, the skew Pieri rule and the skew Murnaghan-Nakayama rule, to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power
Matjaž Konvalinka
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The Schur transform of a generalized Schur function and operator realizations [PDF]
, 2005 Het proefschrift van Gerald Wanjala bouwt voort op werk van de wiskundige Issai Schur uit het begin van de vorige eeuw. Destijds vormde dit het beginpunt van een nieuw onderdeel in de wiskunde: de Schur-analyse.
Wanjala, Gerald, +3 more
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Powers of the Vandermonde determinant, Schur functions, and the dimension game [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions.
Cristina Ballantine
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Multiplicity Free Schur, Skew Schur, and Quasisymmetric Schur Functions [PDF]
Annals of Combinatorics, 2013 In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F-multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and
Bessenrodt, C., van Willigenburg, S.
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Dual Equivalence Graphs Revisited [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's fundamental quasisymmetric ...
Austin Roberts
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The European Physical Journal C, 2023 AbstractWe wonder if there is a way to make all Schur functions in all representations equal. This is impossible for fixed value of time variables, but can be achieved for averages. It appears that the corresponding measure is just Gaussian in times, which are all independent.
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Schur-Convexity for a Class of Symmetric Functions and Its Applications
Journal of Inequalities and Applications, 2009 For x=(x1,x2,…,xn)∈R+n, the symmetric function ϕn(x,r) is defined by ϕn(x,r)=ϕn(x1,x2,…,xn;r)=∏1≤i1<i2⋯<ir≤n(∑j=1r(xij/(1+xij)))1/r, where r=1,2,…,n and i1 ...
Wei-Feng Xia, Yu-Ming Chu
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