Skip to Main content Skip to Navigation
Conference papers

Generalized monotone triangles

Abstract : In a recent work, the combinatorial interpretation of the polynomial $\alpha (n; k_1,k_2,\ldots,k_n)$ counting the number of Monotone Triangles with bottom row $k_1 < k_2 < ⋯< k_n$ was extended to weakly decreasing sequences $k_1 ≥k_2 ≥⋯≥k_n$. In this case the evaluation of the polynomial is equal to a signed enumeration of objects called Decreasing Monotone Triangles. In this paper we define Generalized Monotone Triangles – a joint generalization of both ordinary Monotone Triangles and Decreasing Monotone Triangles. As main result of the paper we prove that the evaluation of $\alpha (n; k_1,k_2,\ldots,k_n)$ at arbitrary $(k_1,k_2,\ldots,k_n) ∈ \mathbb{Z}^n$ is a signed enumeration of Generalized Monotone Triangles with bottom row $(k_1,k_2,\ldots,k_n)$. Computational experiments indicate that certain evaluations of the polynomial at integral sequences yield well-known round numbers related to Alternating Sign Matrices. The main result provides a combinatorial interpretation of the conjectured identities and could turn out useful in giving bijective proofs.
Document type :
Conference papers
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:19:40 AM
Last modification on : Thursday, July 4, 2019 - 3:30:08 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:34:53 AM


Publisher files allowed on an open archive


  • HAL Id : hal-01229671, version 1



Lukas Riegler. Generalized monotone triangles. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.647-658. ⟨hal-01229671⟩



Record views


Files downloads