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Projective embeddings of M‾0,n and parking functions
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2021-05-04 , DOI: 10.1016/j.jcta.2021.105471
Renzo Cavalieri , Maria Gillespie , Leonid Monin

The moduli space M0,n may be embedded into the product of projective spaces P1×P2××Pn3, using a combination of the Kapranov map |ψn|:M0,nPn3 and the forgetful maps πi:M0,iM0,i1. We give an explicit combinatorial formula for the multidegree of this embedding in terms of certain parking functions of height n3. We use this combinatorial interpretation to show that the total degree of the embedding (thought of as the projectivization of its cone in A2×A3×An2) is equal to (2(n3)1)!!=(2n7)(2n9)(5)(3)(1). As a consequence, we also obtain a new combinatorial interpretation for the odd double factorial.



中文翻译:

的投影嵌入 中号0ñ 和停车功能

模空间 中号0ñ 可能嵌入到射影空间的产品中 P1个×P2个××Pñ-3,结合使用Kapranov地图 |ψñ|中号0ñPñ-3 和健忘的地图 π一世中号0一世中号0一世-1个。我们根据高度的某些泊车函数,为该嵌入的多度给出了一个明确的组合公式。ñ-3。我们使用这种组合解释来表明嵌入的总程度(被认为是其圆锥的投影一种2个×一种3×一种ñ-2个)等于 2个ñ-3-1个=2个ñ-72个ñ-9531个。结果,我们也获得了对奇数双阶乘的新组合解释。

更新日期:2021-05-04
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