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pro vyhledávání: '"Gillespie, Maria"'
We prove that the symmetric function $\Delta'_{e_{k-1}}e_n$ appearing in the Delta Conjecture can be obtained from the symmetric function in the Rational Shuffle Theorem by applying a Schur skewing operator. This generalizes a formula by the first an
Externí odkaz:
http://arxiv.org/abs/2408.12543
Autor:
Gillespie, Maria
We introduce higher Specht polynomials - analogs of Specht polynomials in higher degrees - in two sets of variables $x_1,\ldots,x_n$ and $y_1,\ldots,y_n$ under the diagonal action of the symmetric group $S_n$. This generalizes the classical Specht po
Externí odkaz:
http://arxiv.org/abs/2402.05221
Autor:
Gillespie, Maria, Levinson, Jake
In this note, we give a simple closed formula for an arbitrary product, landing in dimension 0, of boundary classes on the Deligne--Mumford moduli space M_0,n-bar. For any such boundary strata $X_{T_1}, \ldots, X_{T_\ell}$, we show the intersection p
Externí odkaz:
http://arxiv.org/abs/2311.09557
Autor:
Gillespie, Maria, Griffin, Sean T.
We prove that $\omega \Delta'_{e_{k}}e_n|_{t=0}$, the symmetric function in the Delta Conjecture at $t=0$, is a skewing operator applied to a Hall-Littlewood polynomial, and generalize this formula to the Frobenius series of all $\Delta$-Springer mod
Externí odkaz:
http://arxiv.org/abs/2307.02645
Monin and Rana conjectured a set of equations defining the image of the moduli space $\bar{M}_{0,n}$ under an embedding into $\mathbb{P}^1\times \cdots\times \mathbb{P}^{n-3}$ due to Keel and Tevelev and verified the conjecture for $n\leq 8$ using Ma
Externí odkaz:
http://arxiv.org/abs/2209.06688
We consider products of $\psi$ classes and products of $\omega$ classes on $\overline{M}_{0,n+3}$. For each product, we construct a flat family of subschemes of $\overline{M}_{0,n+3}$ whose general fiber is a complete intersection representing the pr
Externí odkaz:
http://arxiv.org/abs/2201.07416
Autor:
Gillespie, Maria, Reimer-Berg, Andrew
We give a combinatorial proof of a recent geometric result of Farkas and Lian on linear series on curves with prescribed incidence conditions. The result states that the expected number of degree-$d$ morphisms from a general genus $g$, $n$-marked cur
Externí odkaz:
http://arxiv.org/abs/2201.00416
This textbook, "Counting Rocks!", is the written component of an interactive introduction to combinatorics at the undergraduate level. Throughout the text, we link to videos where we describe the material and provide examples. The major topics in thi
Externí odkaz:
http://arxiv.org/abs/2108.04902
We provide a new geometric interpretation of the multidegrees of the (iterated) Kapranov embedding $\Phi_n:\overline{M}_{0,n+3}\hookrightarrow \mathbb{P}^1\times \mathbb{P}^2\times \cdots \times \mathbb{P}^n$, where $\overline{M}_{0,n+3}$ is the modu
Externí odkaz:
http://arxiv.org/abs/2108.00050