Zobrazeno 1 - 10
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pro vyhledávání: '"Morales A. H"'
We study random permutations arising from reduced pipe dreams. Our main model is motivated by Grothendieck polynomials with parameter $\beta=1$ arising in K-theory of the flag variety. The probability weight of a permutation is proportional to the pr
Externí odkaz:
http://arxiv.org/abs/2407.21653
Publikováno v:
EPTCS 403, 2024, pp. 150-155
We show that coefficients in unicellular LLT polynomials are evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements. We express these in terms of traditional trace bases, induction, and Kazhdan-Lusztig R-polynomials.
Comment: In P
Comment: In P
Externí odkaz:
http://arxiv.org/abs/2406.16414
Autor:
Leake, Jonathan, Morales, Alejandro H.
The type $A$ Kostant partition function is an important combinatorial object with various applications: it counts integer flows on the complete directed graph, computes Hilbert series of spaces of diagonal harmonics, and can be used to compute weight
Externí odkaz:
http://arxiv.org/abs/2406.07838
Standard tableaux of skew shape are fundamental objects in enumerative and algebraic combinatorics and no product formula for the number is known. In 2014, Naruse gave a formula (NHLF) as a positive sum over excited diagrams of products of hook-lengt
Externí odkaz:
http://arxiv.org/abs/2311.09209
We give uniform formulas for the number of full reflection factorizations of a parabolic quasi-Coxeter element in a Weyl group or complex reflection group, generalizing the formula for the genus-0 Hurwitz numbers. This paper is the culmination of a s
Externí odkaz:
http://arxiv.org/abs/2308.04751
In 1999, Pitman and Stanley introduced the polytope bearing their name along with a study of its faces, lattice points, and volume. The Pitman-Stanley polytope is well-studied due to its connections to probability, parking functions, the generalized
Externí odkaz:
http://arxiv.org/abs/2307.09925
Autor:
D'León, Rafael S. González, Morales, Alejandro H., Philippe, Eva, Jiménez, Daniel Tamayo, Yip, Martha
Ceballos and Pons introduced the $s$-weak order on $s$-decreasing trees, for any weak composition $s$. They proved that it has a lattice structure and further conjectured that it can be realized as the $1$-skeleton of a polyhedral subdivision of a po
Externí odkaz:
http://arxiv.org/abs/2307.03474
Autor:
Escobar, Laura, Gallardo, Patricio, González-Anaya, Javier, González, José L., Montúfar, Guido, Morales, Alejandro H.
We investigate the combinatorics of max-pooling layers, which are functions that downsample input arrays by taking the maximum over shifted windows of input coordinates, and which are commonly used in convolutional neural networks. We obtain results
Externí odkaz:
http://arxiv.org/abs/2209.14978
Combinatorial and Algebraic Enumeration: a survey of the work of Ian P. Goulden and David M. Jackson
In this survey we discuss some of the significant contributions of Ian Goulden and David Jackson in the areas of classical enumeration, symmetric functions, factorizations of permutations, and algebraic foundations of quantum field theory. Through th
Externí odkaz:
http://arxiv.org/abs/2209.10075
Publikováno v:
Journal of Algebra, vol. 641 (2024), pp. 648-715
We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the collections $\operatorname{Red}_W(g)$ of reduced r
Externí odkaz:
http://arxiv.org/abs/2209.00066