相关论文: A bijection between symmetric plane partitions and…
This note introduces some bijections relating core partitions and tuples of integers. We apply these bijections to count the number of cores with various types of restriction, including fixed number of parts, limited size of parts, parts…
In this paper, we construct a bijection from a set of bounded free Motzkin paths to a set of bounded Motzkin prefixes that induces a bijection from a set of bounded free Dyck paths to a set of bounded Dyck prefixes. We also give bijections…
The $k$-vertex disjoint paths problem is one of the most studied problems in algorithmic graph theory. In 1994, Schrijver proved that the problem can be solved in polynomial time for every fixed $k$ when restricted to the class of planar…
We present a study of three families of Kronecker coefficients, which we describe in terms of reduced Kronecker coefficients. This study is grounded on the generating function of the coefficients, proved by a bijection between two…
A new algorithm for inserting rim-hooks into reverse plane partitions is presented. The insertion is used to define a bijection between reverse plane partitions of a fixed shape and multi-sets of rim-hooks. In turn this yields a bijective…
We develop the connection of Berg partitions with special substitution tilings of two tiles. We obtain a new proof that the number of Berg partitions with a fixed connectivity matrix is equal to half of the sum of its entries, \cite{S-W}.…
Consider a problem where we are given a bipartite graph H with vertices arranged on two horizontal lines in the plane, such that the two sets of vertices placed on the two lines form a bipartition of H. We additionally require that H admits…
This short note gives a bijection between quarter plane walks using the steps $\{\rightarrow, \searrow, \downarrow, \leftarrow, \nwarrow, \uparrow\}$ and bicoloured Motzkin paths.
We present a combinatorial model of configuration spaces and polytopes associated to the quotients of $\mathbb{C} A_n$, the path algebra of the linearly oriented $A_n$ quiver, i.e. the algebra of upper triangular matrices. These quotient…
To do homological algebra with unbounded chain complexes one needs to first find a way of constructing resolutions. Spaltenstein solved this problem for chain complexes of R-modules by truncating further and further to the left, resolving…
Given a bipartite graph $G=(V_b,V_r,E)$, the $2$-Level Quasi-Planarity problem asks for the existence of a drawing of $G$ in the plane such that the vertices in $V_b$ and in $V_r$ lie along two parallel lines $\ell_b$ and $\ell_r$,…
We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of $m$ mass distributions on $\mathbb{R}^n$, the existence of $k$ affinely independent regular…
Given a finite acyclic quiver Q with path algebra kQ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod kQ and they have…
Motivated by Andrews' recent work related to Euler's partition theorem, we consider the set of partitions of an integer $n$ where the set of even parts has exactly $j$ elements, versus the set of partitions of $n$ where the set of repeated…
Partition theory abounds with bijections between different types of partitions. One of the most famous partition bijections maps each self-conjugate partition of a positive integer $n$ to a partition of $n$ into distinct odd parts, and vice…
Noting a curious link between Andrews' even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer partitions with parts separated by parity. Our motivation is…
In this note, we give a simple extension map from partitions of subsets of [n] to partitions of [n+1], which sends $\delta$-distant k-crossings to $(\delta+1)$-distant k-crossings (and similarly for nestings). This map provides a…
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
In a recent article Halpern-Leistner defines the notion of quasi--convergent path in the space of Bridgeland stability conditions. Such a path induces a semiorthogonal decomposition of the derived category. We investigate quasi-convergent…
It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life, to address this issue, we studied…