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A complete solution to the biased Alon-Krivelevich-Spencer-Szabó criterion problem for the discrepancy game Krahn-Szegő type inequalities for graphs $\boldsymbol{2}$-Neighbor Bootstrap Percolation on Odd Graphs Modular inequalities and Alexander polynomials of pencil type conic-line arrangements Counterexamples regarding elementary symmetric partitions Bounds on Multiple $b$-Burst Deletion-Correcting Codes The mex statistic on combinatorial structures Proper Additive Edge Colorings of Regular Graphs Off-diagonal Ramsey numbers Extremality in semidistributive lattices Three formulas for CSM classes of open quiver loci Roman $\{2\}$-domination on Graphs with "few" 4-paths Circularity and Symmetries of $p$ and $p^{2}$-polygons Finding Kissing Numbers with Game-theoretic Reinforcement Learning Directed Hamiltonicity in Generalized Kneser Graphs Inferring DAGs and Phylogenetic Networks from Least Common Ancestors Additive structures imply more distances in $\mathbb{F}_q^d$ Semi-inducibility of 4-vertex graphs A Structural Condition on Point Sets with Few Distinct Dot Products A quantum N-dimer model Möbius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs Well quasi-order and atomicity for combinatorial structures under consecutive orders The Permanent Rank of a Matrix (Part Three) Note on the Additive Basis Conjecture Complexity of the Zero Set of a Matrix Schubert Ideal The existence of unexpected automorphisms in direct product graphs Reconstruction of oriented matroids from Varchenko-Gelfand algebras Addition theorems for Ziegler pairs of hyperplane arrangements Combinatorial proofs of Petrie Pieri rule and Plethystic Pieri rule Asymptotic structure. 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Multigraded Betti numbers of Veronese embeddings
Christian Haase, Zongpu Zhang · 2025-11-24 · via math.CO updates on arXiv.org

In this paper, we study the multigraded Betti numbers of Veronese embeddings of projective spaces. Due to Hochster's formula, we interpret these multigraded Betti numbers in terms of the homology of certain simplicial complexes. By analyzing these simplicial complexes and applying Forman's discrete Morse theory, we derive vanishing and non-vanishing results for these multigraded Betti numbers.

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