Concept
Enumerative combinatorics
Publications associées (21)
Non-planarity of Markoff graphs mod p
We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...
Berlin2024Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths
In this paper we study the moments of polynomials from the Askey scheme, and we focus on Askey-Wilson polynomials. More precisely, we give a combinatorial proof for the case where d = 0. Their values have already been computed by Kim and Stanton in 2015, h ...
ELECTRONIC JOURNAL OF COMBINATORICS2021Enumeration of reversible functions and its application to circuit complexity
Giovanni De Micheli, Mathias Soeken, Nabila Abdessaied
We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying li ...
Springer2016Homology of the three flag Hilbert Scheme
We prove the existence of an affine paving for the three-step flag Hilbert scheme that parametrizes flag of three 0-dimensional subschemes of length, respectively, n, n+1 and n+2 that are supported at the origin of the affine plane. This is done by showing ...
EPFL2016Programming with Enumerable Sets of Structures
Viktor Kuncak, Ivan Kuraj, Daniel Jackson
We present an efficient, modular, and feature-rich framework for automated generation and validation of complex structures, suitable for tasks that explore a large space of structured values. Our framework is capable of exhaustive, incremental, parallel, a ...
Assoc Computing Machinery2015Moment Semantics for Reversible Rule-Based Systems
We develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the ‘no-dangling-edge’ con ...
Springer International Publishing2015