Related papers: P\'olya theory for species with an equivariant gro…
We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.
The genus spectrum of a finite group $G$ is the set of all $g$ such that $G$ acts faithfully on a compact Riemann surface of genus $g$. It is an open problem to find a general description of the genus spectrum of the groups in interesting…
We give noncommutative versions of the Redfield-P\'olya theorem in WSym, the algebra of word symmetric functions, and in other related combinatorial Hopf algebras.
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
P-algebras are a non-commutative, non-associative generalization of Boolean algebras that are for quantum logic what Boolean algebras are for classical logic. P-algebras have type <X, 0, ', .> where 0 is a constant, ' is unary and . is…
Recent development of path integral matching techniques based on the covariant derivative expansion has made manifest a universal structure of one-loop effective Lagrangians. The universal terms can be computed once and for all to serve as…
We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally equivalences of groupoids. Key features of combinatorial…
Bayesian hierarchical models are used to share information between related samples and obtain more accurate estimates of sample-level parameters, common structure, and variation between samples. When the parameter of interest is the…
Imprimitivity theorems provide a fundamental tool for studying the representation theory and structure of crossed-product C*-algebras. In this work, we show that the Imprimitivity Theorem for induced algebras, Green's Imprimitivity Theorem…
A common framework is provided that comprises classical ordinal item response models as the cumulative, sequential and adjacent categories models as well as nominal response models and item response tree models. The taxonomy is based on the…
We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory" for complex algebraic varieties. The theory is bigraded, functorial,…
This work presents a detailed analysis of the combinatorics of modular operads. These are operad-like structures that admit a contraction operation as well as an operadic multiplication. Their combinatorics are governed by graphs that admit…
In "Meromorphic Functions and Analytic Curves", H. and F. J. Weyl identified an intriguing connection between holomorphic curves and their associated curves, which they referred to as the "peculiar relation". In this paper, we present a…
Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding…
The action of a Weyl group on the associated weight lattice induces an additive action on the symmetric algebra and a multiplicative action on the group algebra of the lattice. We show that the coinvariant space of the multiplicative action…
We extend P\'olya's indicator diagram theory to encompass entire functions of order at most 1, allowing functions of maximal type. To do so, we introduce an extension of the complex plane in which indicator diagrams may be unbounded or even…
In symmetric groups, studies of permutation factorizations or triples of permutations satisfying certain conditions have a long history. One particular interesting case is when two of the involved permutations are long cycles, for which…
This work is devoted to P\'olya-Young urns, a class of periodic P\'olya urns of importance in the analysis of Young tableaux. We provide several extension of the previous results of Banderier, Marchal and Wallner [Ann. Prob. (2020)] on…
For non-negative integers $k\leq n$, we prove a combinatorial identity for the $p$-binomial coefficient $\binom{n}{k}_p$ based on abelian p-groups. A purely combinatorial proof of this identity is not known. While proving this identity, for…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…