2 citations · 9 across the 14 of their papers we have counts for
15 papers
Coefficient lifting for skew divided differences and triple Schubert coefficients
Byung-Hak Hwang
Skew divided difference operators \(\partial_{w/v}\), introduced by Macdonald, play an important role in the study of Schubert polynomials and their structure constants. For permut…
A Computational Obstruction to Swapping Area and Dinv: An Automata-Theoretic View of the -Catalan Symmetry
Jineon Baek, Byung-Hak Hwang, Joonhyun La +1
Algebraic combinatorics often seeks bijections that explain identities between distributions object by object. Encoding combinatorial objects as words lets automata theory study su…
Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
Seewoo Lee, Byung-Hak Hwang, Hyojae Lim +10
We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pi…
A sign-reversing involution for the antipode of Schur functions
Younggwang Cho, Byung-Hak Hwang, Hojoon Lee
We resolve a question posed by Benedetti and Sagan by constructing a signreversing involution on Takeuchi's expansion that yields the antipode for the ring of symmetric functions i…
Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified
Martin Dvorak, Tristan Figueroa-Reid, Rida Hamadani +8
Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory fa…
Refinement of Hikita's -positivity theorem via Abreu--Nigro's -functions and restricted modular law
JiSun Huh, Byung-Hak Hwang, Donghyun Kim +2
We study the symmetric functions \( g_{\mm,k}(x;q) \), introduced by Abreu and Nigro for a Hessenberg function \( \mm \) and a positive integer \( k \), which refine the chromatic…
Refined canonical stable Grothendieck polynomials and their duals, Part 2
Byung-Hak Hwang, Jihyeug Jang, Jang Soo Kim +2
This paper is the sequel of the paper under the same title with part 1, where we introduced refined canonical stable Grothendieck polynomials and their duals with two families of i…
Noncommutative symmetric functions and skewing operators
Byung-Hak Hwang
Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutat…
Chromatic quasisymmetric functions and noncommutative -symmetric functions
Byung-Hak Hwang
For a natural unit interval order , we describe proper colorings of the incomparability graph of in the language of heaps. We also introduce a combinatorial operation, calle…
A combinatorial model for the transition matrix between the Specht and web bases
Byung-Hak Hwang, Jihyeug Jang, Jaeseong Oh
We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between…
Refined canonical stable Grothendieck polynomials and their duals, Part 1
Byung-Hak Hwang, Jihyeug Jang, Jang Soo Kim +2
In this paper we introduce refined canonical stable Grothendieck polynomials and their duals with two infinite sequences of parameters. These polynomials unify several generalizati…
Ribbon tiling and character formula for periplectic Lie superalgebras
Byung-Hak Hwang, Jae-Hoon Kwon
We give a combinatorial formula for the character of a finite-dimensional irreducible representation of the periplectic Lie superalgebra . The character of irreduc…
On linearization coefficients of -Laguerre polynomials
Byung-Hak Hwang, Jang Soo Kim, Jaeseong Oh +1
The linearization coefficient of classical Laguerre polynomials is known to be equal to the number of -derangeme…
Acyclic orientation polynomials and the sink theorem for chromatic symmetric functions
Byung-Hak Hwang, Woo-Seok Jung, Kang-Ju Lee +2
We define the acyclic orientation polynomial of a graph to be the generating function for the sinks of its acyclic orientations. Stanley proved that the number of acyclic orientati…
Reverse plane partitions of skew staircase shapes and -Euler numbers
Byung-Hak Hwang, Jang Soo Kim, Meesue Yoo +1
Recently, Naruse discovered a hook length formula for the number of standard Young tableaux of a skew shape. Morales, Pak and Panova found two -analogs of Naruse's hook length f…