Ricky Ini Liu
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View article: Piecewise-linear promotion and RSK in rectangles and moon polyominoes
Piecewise-linear promotion and RSK in rectangles and moon polyominoes Open
View article: Generalized degree polynomials of trees
Generalized degree polynomials of trees Open
The generalized degree polynomial $\mathbf{G}_T(x,y,z)$ of a tree $T$ is an invariant introduced by Crew that enumerates subsets of vertices by size and number of internal and boundary edges. Aliste-Prieto et al. proved that $\mathbf{G}_T$…
View article: Birational rowmotion and the octahedron recurrence
Birational rowmotion and the octahedron recurrence Open
We use the octahedron recurrence to give a simplified statement and proof of a formula for iterated birational rowmotion on a product of two chains, first described by Musiker and Roby. Using this, we show that weights of certain chains in…
View article: Plane partitions and rowmotion on rectangular and trapezoidal posets
Plane partitions and rowmotion on rectangular and trapezoidal posets Open
We define a birational map between labelings of a rectangular poset and its associated trapezoidal poset. This map tropicalizes to a bijection between the plane partitions of these posets of fixed height, giving a new bijective proof of a …
View article: Shuffle Bases and Quasisymmetric Power Sums
Shuffle Bases and Quasisymmetric Power Sums Open
The algebra of quasisymmetric functions QSym and the shuffle algebra of compositions Sh are isomorphic as graded Hopf algebras (in characteristic zero), and isomorphisms between them can be specified via shuffle bases of QSym. We use the n…
View article: Placenta-Derived Extracellular Vesicles From Preeclamptic Pregnancies Impair Vascular Endothelial Function via Lectin-Like Oxidized LDL Receptor-1
Placenta-Derived Extracellular Vesicles From Preeclamptic Pregnancies Impair Vascular Endothelial Function via Lectin-Like Oxidized LDL Receptor-1 Open
BACKGROUND: Preeclampsia is a complex syndrome that includes maternal vascular dysfunction. Syncytiotrophoblast-derived extracellular vesicles from preeclampsia placentas (preeclampsia-STBEVs) were shown to induce endothelial dysfunction, …
View article: The Long-Term Effects of Prenatal Hypoxia on Coronary Artery Function of the Male and Female Offspring
The Long-Term Effects of Prenatal Hypoxia on Coronary Artery Function of the Male and Female Offspring Open
Prenatal hypoxia predisposes the offspring to the development of cardiovascular (CV) dysfunction in adult life. Using a rat model, we assessed the effect of prenatal hypoxia on vasoconstrictive and vasodilative mechanisms in left anterior …
View article: Placenta-derived extracellular vesicles from preeclamptic and healthy pregnancies impair <i>ex vivo</i> vascular endothelial function
Placenta-derived extracellular vesicles from preeclamptic and healthy pregnancies impair <i>ex vivo</i> vascular endothelial function Open
Preeclampsia (PE) is a pregnancy syndrome characterized by new-onset hypertension and end-organ dysfunction. The pathophysiology of PE remains undetermined, but it is thought that maternal vascular dysfunction plays a central role, potenti…
View article: Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes
Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes Open
Gelfand-Tsetlin polytopes are classical objects in algebraic combinatorics arising in the representation theory of \(\mathfrak{gl}_n(\mathbb{C})\). The integer point transform of the Gelfand-Tsetlin polytope \(\mathrm{GT}(\lambda)\) projec…
View article: Piecewise-linear promotion and RSK in rectangles and moon polyominoes
Piecewise-linear promotion and RSK in rectangles and moon polyominoes Open
We study piecewise-linear and birational lifts of Schützenberger promotion, evacuation, and the RSK correspondence defined in terms of toggles. Using this perspective, we prove that certain chain statistics in rectangles shift predictably …
View article: Birational Rowmotion and the Octahedron Recurrence
Birational Rowmotion and the Octahedron Recurrence Open
We use the octahedron recurrence to give a simplified statement and proof of a formula for iterated birational rowmotion on a product of two chains, first described by Musiker and Roby. Using this, we show that weights of certain chains in…
View article: Determinantal Formulas for SEM Expansions of Schubert Polynomials
Determinantal Formulas for SEM Expansions of Schubert Polynomials Open
View article: Up- and Down-Operators on Young's Lattice
Up- and Down-Operators on Young's Lattice Open
The up-operators $u_i$ and down-operators $d_i$ (introduced as Schur operators by Fomin) act on partitions by adding/removing a box to/from the $i$th column if possible. It is well known that the $u_i$ alone satisfy the relations of the (l…
View article: Channels, Billiards, and Perfect Matching 2-Divisibility
Channels, Billiards, and Perfect Matching 2-Divisibility Open
Let $m_G$ denote the number of perfect matchings of the graph $G$. We introduce a number of combinatorial tools for determining the parity of $m_G$ and giving a lower bound on the power of 2 dividing $m_G$. In particular, we introduce cert…
View article: P-partition generating function equivalence of naturally labeled posets
P-partition generating function equivalence of naturally labeled posets Open
View article: The Algebra of Schur Operators
The Algebra of Schur Operators Open
We study a representation of the (local) plactic monoid given by Schur operators $u_i$, which act on partitions by adding a box in column $i$ (if possible). In particular, we give a complete list of the relations that hold in the algebra o…
View article: Twisted Schubert polynomials
Twisted Schubert polynomials Open
We prove that twisted versions of Schubert polynomials defined by $\widetilde{\mathfrak S}_{w_0} = x_1^{n-1}x_2^{n-2} \cdots x_{n-1}$ and $\widetilde{\mathfrak S}_{ws_i} = (s_i+\partial_i)\widetilde{\mathfrak S}_w$ are monomial positive an…
View article: Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes
Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes Open
Gelfand-Tsetlin polytopes are classical objects in algebraic combinatorics arising in the representation theory of $\mathfrak{gl}_n(\mathbb{C})$. The integer point transform of the Gelfand-Tsetlin polytope $\mathrm{GT}(λ)$ projects to the …
View article: $P$-Partitions and Quasisymmetric Power Sums
$P$-Partitions and Quasisymmetric Power Sums Open
The $(P, ω)$-partition generating function of a labeled poset $(P, ω)$ is a quasisymmetric function enumerating certain order-preserving maps from $P$ to $\mathbb{Z}^+$. We study the expansion of this generating function in the recently in…
View article: Gelfand--Tsetlin Polytopes: A Story of Flow and Order Polytopes
Gelfand--Tsetlin Polytopes: A Story of Flow and Order Polytopes Open
Gelfand-Tsetlin polytopes are prominent objects in algebraic combinatorics. The number of integer points of the Gelfand-Tsetlin polytope $\mathrm{GT}(λ)$ is equal to the dimension of the corresponding irreducible representation of $GL(n)$.…
View article: $P$-Partition Generating Function Equivalence of Naturally Labeled\n Posets
$P$-Partition Generating Function Equivalence of Naturally Labeled\n Posets Open
The $P$-partition generating function of a (naturally labeled) poset $P$ is a\nquasisymmetric function enumerating order-preserving maps from $P$ to\n$\\mathbb{Z}^+$. Using the Hopf algebra of posets, we give necessary conditions\nfor two …
View article: Kronecker coefficients and noncommutative super Schur functions
Kronecker coefficients and noncommutative super Schur functions Open
View article: A simplified Kronecker rule for one hook shape
A simplified Kronecker rule for one hook shape Open
Recently Blasiak has given a combinatorial rule for the Kronecker coefficient when is a hook shape by defining a set of colored Yamanouchi tableaux with cardinality in terms of a process called conversion. We give a characterization of …
View article: Complete branching rules for Specht modules
Complete branching rules for Specht modules Open