arXiv subjects

Bin Bin Han

Publications and source records attributed to Bin Bin Han.

4 recordsLinked to original sources

arXiv2026

Representations and identities of involution Plactic-like monoids arising from the meet of the stalactic congruence and its dual

Let $\mathsf{mSt}_n$ be the plactic-like monoid obtained by factoring the free monoid over a finite alphabet $\mathcal{A}_n$ by the meet of the stalactic congruence and its dual. In this paper, we prove that $\mathsf{mSt}_n$ can be equipped with multiple involutions, and divide these involutions into $\lfloor\frac{n}{2}\rfloor+1$ types. A faithful representation of $\mathsf{mSt}_n$ under each of these involutions is obtained. We give transparent combinatorial characterizations of identities for $\mathsf{mSt}_n$ under each involution, and so the finite basis problem and identity checking problem for them are solved.

math.GR↗

arXiv2023

Representations and identities of hypoplactic monoids with involution

Let $(\mathsf{hypo}_n,~^\sharp)$ be the hypoplactic monoid of finite rank $n$ with Schützenberger's involution $^{\sharp}$. In this paper, we exhibit a faithful representation of $(\mathsf{hypo}_n,~^\sharp)$ as an involution monoid of upper triangular matrices over any semiring from a large class including the tropical semiring under the skew transposition. We then give a transparent combinatorial characterization of the word identities satisfied by $(\mathsf{hypo}_n,~^\sharp)$. Further, we prove that $(\mathsf{hypo}_n,~^\sharp)$ is non-finitely based if and only if $n=2, 3$ and give a polynomial time algorithm to check whether a given word identity holds in $(\mathsf{hypo}_n,~^\sharp)$.

math.RT↗

arXiv2023

Representations and identities of Baxter monoids with involution

Let $(\mathsf{baxt}_n,~^\sharp)$ be the Baxter monoid of finite rank $n$ with Schützenberger's involution $^{\sharp}$. In this paper, it is shown that $(\mathsf{baxt}_n,~^\sharp)$ admits a faithful representation by an involution monoid of upper triangular matrices over any semiring from a large class including the tropical semiring under the skew transposition. Then a transparent combinatorial characterization of the word identities satisfied by $(\mathsf{baxt}_n,~^\sharp)$ is given. Further, it is proved that $(\mathsf{baxt}_n,~^\sharp)$ is finitely based if and only if $n\neq 3$, and shown that the identity checking problem for $(\mathsf{baxt}_n,~^\sharp)$ can be done in polynomial time.

math.GR↗

arXiv2021

Finite basis problems for stalactic, taiga, sylvester and Baxter monoids

Stalactic, taiga, sylvester and Baxter monoids arise from the combinatorics of tableaux by identifying words over a fixed ordered alphabet whenever they produce the same tableau via some insertion algorithm. In this paper, three sufficient conditions under which semigroups are finitely based are given. By applying these sufficient conditions, it is shown that all stalactic and taiga monoids of rank greater than or equal to $2$ are finitely based and satisfy the same identities, that all sylvester monoids of rank greater than or equal to $2$ are finitely based and satisfy the same identities and that all Baxter monoids of rank greater than or equal to $2$ are finitely based and satisfy the same identities.

math.GR↗