-partition boards and poly-Stirling numbers.
Major indices and perfect bases for complex reflection groups.
Matrices connected with Brauer's centralizer algebras.
Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we...
Matrix realizations of pairs of Young tableaux, keys and shuffles.
Matrix tableau-pairs with key and shuffling conditions.
Maximal projective degrees for strict partitions.
Metric coset schemes revisited
An Abelian scheme corresponds to a special instance of what is usually named a Schur-ring. After the needed results have been quoted on additive codes in Abelian schemes and their duals, coset configurations, coset schemes, metric schemes and distance regular graphs, partition designs and completely regular codes, we give alternative proofs of some of those results. In this way we obtain a construction of metric Abelian schemes and an algorithm to compute their intersection matrices.
Metrically regular square of metrically regular bigraphs. I
Metrically regular square of metrically regular bigraphs. II.
Metrically regular bigraphs the square of which are metrically regular graphs are investigated in the case of graphs with 6 distinct eigenvalues (these eigenvalues can have variuos multiplicities).
Metrically regular square of metrically regular bipartite graphs of diameter
The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter see [7] and [8].
Minimality of toric arrangements
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.
Minuscule heaps over Dynkin diagrams of type .
Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)
Modular invariance property of association schemes is recalled in connection with our joint work with François Jaeger. Then we survey codes over discussing how codes, through their (various kinds of) weight enumerators, are related to (various kinds of) modular forms through polynomial invariants of certain finite group actions and theta series. Recently, not only codes over an arbitrary finite field but also codes over finite rings and finite abelian groups are considered and have been studied...
Modulo study of the mahonian statistics. (Étude modulo des statistiques mahoniennes.)
Moment polytopes of projective -varieties and tensor products of symmetric group representations.
Monomial crystals and partition crystals.
Monomial ideals with tiny squares and Freiman ideals
We provide a construction of monomial ideals in such that , where denotes the least number of generators. This construction generalizes the main result of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018). Working in the ring , we generalize the definition of a Freiman ideal which was introduced in J. Herzog, G. Zhu (2019) and then we give a complete characterization of such ideals. A particular case of this characterization leads to some further investigations on that generalize some results...
Monomial nonnegativity and the Bruhat order.
Monotone Hurwitz Numbers and the HCIZ Integral
In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of . Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.