Zobrazeno 1 - 10
of 982
pro vyhledávání: '"Morales, Alejandro"'
Autor:
Morales, Alejandro H., Shi, William
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 7, Pp 823-851 (2021)
Flow polytopes are an important class of polytopes in combinatorics whose lattice points and volumes have interesting properties and relations. The Chan–Robbins–Yuen (CRY) polytope is a flow polytope with normalized volume equal to the product of
Externí odkaz:
https://doaj.org/article/68bf537ba2d549b79d8dc475bab81e9a
We show by an explicit example that the Garsia--Remmel $q$-rook numbers of Ferrers boards do not all have unimodal sequences of coefficients. This resolves in the negative a question from 1986 by the aforementioned authors.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2410.19714
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