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Oberwolfach Reports, 2023 The Department of Mathematics at Harvey Mudd College will host its 8t annual Mathematics Conference on Saturday, October 7, 2006. Keynote speakers will discuss new developments and applications of enumerative combinatorics. Faculty, postdoctoral fellows
Mireille Bousquet-Mélou +3 more
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Combinatorics and preservation of conically stable polynomials [PDF]
Journal of Algebraic Combinatorics, 2022 Given a closed, convex cone $$K\subseteq \mathbb {R}^n$$ K ⊆ R n , a multivariate polynomial $$f\in \mathbb {C}[\textbf{z}]$$ f ∈ C [ z ] is called K -stable if the imaginary parts of its roots are not contained in the relative interior of K .
Giulia Codenotti +2 more
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Some results on counting roots of polynomials and the Sylvester resultant. [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We present two results, the first on the distribution of the roots of a polynomial over the ring of integers modulo n and the second on the distribution of the roots of the Sylvester resultant of two multivariate polynomials.
Michael Monagan, Baris Tuncer
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Almost simplicial polytopes: the lower and upper bound theorems [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 this is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes.
Eran Nevo +3 more
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Canonical Characters on Quasi-Symmetric Functions and Bivariate Catalan Numbers [PDF]
Electronic Journal of Combinatorics, 2004 Every character on a graded connected Hopf algebra decomposes uniquely as a product of an even character and an odd character (Aguiar, Bergeron, and Sottile, math.CO/0310016).
M. Aguiar, Samuel K. Hsiao
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Oberwolfach Reports, 2023 . It is known that the complex Grassmannian of k -dimensional sub-spaces can be identified with the set of projection matrices of rank k . It is also classically known that the convex hull of this set is the set of Hermitian matrices with eigenvalues ...
Peter Keevash +2 more
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Symmetric Fundamental Expansions to Schur Positivity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We consider families of quasisymmetric functions with the property that if a symmetric function f is a positive sum of functions in one of these families, then f is necessarily a positive sum of Schur functions.
Austin Roberts
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Hook formulas for skew shapes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over ...
Alejandro H. Morales +2 more
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The Smith normal form distribution of a random integer matrix [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We show that the density μ of the Smith normal form (SNF) of a random integer matrix exists and equals a product of densities μps of SNF over Z/psZ with p a prime and s some positive integer.
Yinghui Wang, Richard P. Stanley
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On (non-) freeness of some tridendriform algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We present some results on the freeness or non freeness of some tridendriform algebras. In particular, we give a combinatorial proof of the freeness of WQSym, an algebra based on packed words, result already known with an algebraic proof.
Vincent Vong
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