The “classical” parking functions, counted by the Cayley number (n+ 1) n− 1, carry a natural
permutation representation of the symmetric group S n in which the number of orbits is the …

We find a geometric interpretation of the A q, t algebra, the algebra which appeared in the
previous work of Erik Carlsson and the author on the proof of the shuffle conjecture. This …

We examine the set of J b (F)-orbits in the set of irreducible components of affine Deligne–
Lusztig varieties for a hyperspecial subgroup and minuscule coweight μ. Our description …

We repurpose the main theorem of Thomas and Williams (J Algebr Comb 39 (2): 225–246,
2014) to prove that modular sweep maps are bijective. We construct the inverse of the …

Today we live in a society of high technologies, advanced information and communication
systems in every field, including education. So, in modern education, teachers make full use …

This paper introduces a Hopf algebra structure on a family of reduced pipe dreams. We
show that this Hopf algebra is free and cofree, and construct a surjection onto a commutative …

For an irreducible crystallographic root system Φ and a positive integer p relatively prime to
the Coxeter number h of Φ, we give a natural bijection A from the set W˜ p of affine Weyl …

We discuss the combinatorics of the decorated Dyck paths appearing in the Delta conjecture
framework of Haglund, Remmel and Wilson (2015) and Zabrocki (2016), by introducing two …

I present an overview of the research I have conducted for the past ten years in algebraic,
bijective, enumerative, and geometric combinatorics. The two main objects I have studied …

We define two symmetric $ q, t $-Catalan polynomials in terms of the area and depth statistic
and in terms of the dinv and dinv of depth statistics. We prove symmetry using an involution …