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Showing 1 to 20 of 32 for “"Symmetric Functions"”.
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Odd symmetric functions and categorification
… constructions in and around the theory of symmetric functions. The most basic of these is the Hopf superalgebra of odd symmetric functions. This algebra is neither (super-)commutative nor (super-)cocommutative, yet its combinatorics still exhibit many of the striking integrality and …
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Noncommutative symmetric functions of type B
The noncommutative symmetric functions Sym of Gelfand et al. give not only a lifting of the well-developed commutative theory of symmetric functions to the non-commutative level, but also relate the descent algebras of Solomon and the quasi-symmetric functions, where the latter are dual to the …
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A graphical calculus for shifted symmetric functions
… three categori cations of the algebra of symmetric functions and establish relationships between them all. The second goal is to establish an isomorphism between the centre of Khovanov's Heisenberg category [Kho14] and the algebra of shifted symmetric functions defined by Okounkov and …
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A graphical calculus for shifted symmetric functions
… three categori cations of the algebra of symmetric functions and establish relationships between them all. The second goal is to establish an isomorphism between the centre of Khovanov's Heisenberg category [Kho14] and the algebra of shifted symmetric functions defined by Okounkov and …
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The involution principle and h-positive symmetric functions
… linear group of V is a sum of tensor products of symmetric powers of V. Expanding the iterated exponential function as a power series yields coefficients whose positivity implies the h-positivity of the characteristic of the symmetric group character whose value on the permutation w is the number …
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The Complete and Elementary Symmetric Functions as Quotients of Determinants
The standard definition of a Schur symmetric function, is as a quotient of a determinant
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New degrees of freedom in integrable models with q-Hahn weights and their applications to symmetric functions and probability.
… to construct a generalization of t=0 Macdonald symmetric functions, which we call inhomogeneous spin q-Whittaker polynomials. Using integrability we are able to extend several classical properties of symmetric functions to our generalization, in particular, we prove analogues of the Cauchy and …
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Partitions into prime powers and related divisor functions
In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are polynomials over Q in the so-called elementary prime symmetric functions, whose values lie in Z. The latter are defined on the nonnegative integers and take the values of the elementary symmetric …
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Theta Maps for Combinatorial Hopf Algebras
… generalize marked shifted tableaux and Schur's Q functions. Nyman shows that it is a the sum of permutations with the same peak set. Aguiar, Bergeron and Sottile show that the peak algebra is the odd Hopf sub-algebra of quasi symmetric functions using their theory of combinatorial Hopf algebras. …
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Algebraic and combinatorial properties of minimal border strip tableaux
… terms in the expansion of Schur's Q[sub][lambda] symmetric functions in terms of the power sum symmetric functions. The second result gives a basis for the space spanned by the lowest degree terms in the expansion of the Schur symmetric functions in terms of the power sum symmetric functions. …
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Combinatorics of ribbon tableaux
This thesis begins with the study of a class of symmetric functions ... Which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of Fomin and Greene, I introduce a set of operators called ribbon Schur operators …
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Point processes of representation theoretic origin
… In the first part we compute the correlation functions of the 4-parameter family of BC type Z-measures. The result is given explicitly in terms of Gauss's hypergeometric function. The BC type Z-measures are point processes on the punctured positive real line. They arise as interpolations of …
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Partially-Symmetric Macdonald Polynomials
Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald …
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Topology and combinatorics of low genus mapping spaces to projective space
… mixed Hodge structures, tropical moduli spaces, symmetric functions, and the Grothendieck ring of varieties. The results of the thesis extend the structures and results on the moduli spaces of low genus stable curves and genus zero stable maps to projective space, overcoming the subtlety caused …
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Arithmetic of partition functions and q-combinatorics
… theory of modular forms, representation theory, symmetric functions and mathematical physics. Among these, we study the arithmetic of partition functions and q-combinatorics via bijective methods, q-series and modular forms. In particular, regarding arithmetic properties of partition functions, …
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Symmetric Circuits and Model-Theoretic Logics
… the same expressive power as uniform families of symmetric circuits over a basis with threshold functions. In this thesis we prove a far-reaching generalisation of their result and establish an analogous circuit characterisation for each from a broad range of extensions of fixed-point logic. In …
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Specht modules and Schubert varieties for general diagrams
The algebra of symmetric functions, the representation theory of the symmetric group, and the geometry of the Grassmannian are related to each other via Schur functions, Specht modules, and Schubert varieties, all of which are indexed by partitions and their Young diagrams. We will generalize these …
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Wireless Networks for Communication and Sensing
… we propose efficient algorithms for computing symmetric functions over noisy channels. For the data storage problem, we develop distributed algorithms for efficient query processing.
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On total Springer representations
… geometry of Springer fibers and combinatorics of symmetric functions. Moreover, we provide formulas for the character value of a total Springer representation at any element in the stabilizer of the corresponding nilpotent element. For exceptional types, the character values of total Springer …
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Stable characters for symmetric groups and wreath products
… C, say), [mathematical equation] is the ring of symmetric functions. The basis obtained by our construction is the family of stable Specht polynomials, which is closely related to the problem of calculating restriction multiplicities from [mathematical equation]. We categorify the stable Specht …
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