Results 21 to 30 of about 12,508,597 (366)
On e-Positivity and e-Unimodality of Chromatic Quasi-symmetric Functions [PDF]
SIAM Journal on Discrete Mathematics, 2017 The $e$-positivity conjecture and the $e$-unimodality conjecture of chromatic quasisymmetric functions are proved for some classes of natural unit interval orders. Recently, J. Shareshian and M.
Soojin Cho, JiSun Huh
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Lollipop and Lariat Symmetric Functions [PDF]
SIAM Journal on Discrete Mathematics, 2017 We compute an explicit $e$-positive formula for the chromatic symmetric function of a lollipop graph, $L_{m,n}$. From here we deduce that there exist countably infinite distinct $e$-positive, and hence Schur-positive, bases of the algebra of symmetric ...
Samantha Dahlberg, S. Willigenburg
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Branching rules in the ring of superclass functions of unipotent upper-triangular matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical ...
Nathaniel Thiem
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Weakly symmetric functions on spaces of Lebesgue integrable functions
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this work, we present the notion of a weakly symmetric function. We show that the subset of all weakly symmetric elements of an arbitrary vector space of functions is a vector space.
T.V. Vasylyshyn, V.A. Zahorodniuk
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The Chromatic Symmetric Functions of Trivially Perfect Graphs and Cographs [PDF]
Graphs and Combinatorics, 2017 Richard P. Stanley defined the chromatic symmetric function of a simple graph and has conjectured that every tree is determined by its chromatic symmetric function.
Shuhei Tsujie
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NONCOMMUTATIVE SYMMETRIC FUNCTIONS ASSOCIATED WITH A CODE, LAZARD ELIMINATION, AND WITT VECTORS [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 The construction of the universal ring of Witt vectors is related to Lazard's factorizations of free monoids by means of a noncommutative analogue. This is done by associating to a code a specialization of noncommutative symmetric functions.
Jean-Gabriel Luque, Jean-Yves Thibon
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Infinite log-concavity: developments and conjectures [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Given a sequence $(a_k)=a_0,a_1,a_2,\ldots$ of real numbers, define a new sequence $\mathcal{L}(a_k)=(b_k)$ where $b_k=a_k^2-a_{k-1}a_{k+1}$. So $(a_k)$ is log-concave if and only if $(b_k)$ is a nonnegative sequence. Call $(a_k)$ $\textit{infinitely log-
Peter R. W. McNamara, Bruce E. Sagan
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The Murnaghan―Nakayama rule for k-Schur functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We prove a Murnaghan–Nakayama rule for k-Schur functions of Lapointe and Morse. That is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a k-Schur function in terms of k-Schur functions.
Jason Bandlow +2 more
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The Hopf structure of symmetric group characters as symmetric functions [PDF]
Algebraic Combinatorics, 2018 In arXiv:1605.06672 the authors introduced inhomogeneous bases of the ring of symmetric functions. The elements in these bases have the property that they evaluate to characters of symmetric groups.
R. Orellana, M. Zabrocki
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Properties of Meromorphic Spiral-Like Functions Associated with Symmetric Functions
Journal of Function Spaces, 2022 To consolidate or adapt to many studies on meromorphic functions, we define a new subclass of meromorphic functions of complex order involving a differential operator.
Daniel Breaz +3 more
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