Zobrazeno 1 - 10
of 34
pro vyhledávání: '"05A15, 05A20"'
Autor:
Alexandersson, Per, Jal, Aryaman
We define and study rook matroids, the bases of which correspond to non-nesting rook placements on a skew Ferrers board. We show that rook matroids are closed under taking duals, direct sums but not minors. Rook matroids are also transversal, positro
Externí odkaz:
http://arxiv.org/abs/2410.00127
Autor:
Deb, Bishal, Sokal, Alan D.
We prove the coefficientwise Hankel-total positivity of the even and odd subsequences of Schett polynomials $X_n(x,y,z)$.
Comment: LaTeX2e, 12 pages, extended abstract submitted to FPSAC 2024
Comment: LaTeX2e, 12 pages, extended abstract submitted to FPSAC 2024
Externí odkaz:
http://arxiv.org/abs/2311.11747
Autor:
Selig, Thomas, Zhu, Haoyue
In parking problems, a given number of cars enter a one-way street sequentially, and try to park according to a specified preferred spot in the street. Various models are possible depending on the chosen rule for collisions, when two cars have the sa
Externí odkaz:
http://arxiv.org/abs/2309.11788
Autor:
Arab, Mohammad
In this article, we present four issues and provide a creative and concise proof for each of them. The four issues are: 1- Inequality $\frac{1}{\sqrt{n\pi+\frac{\pi}{2}}}<\frac{\binom{2n}{n}}{2^{2n}}<\frac{1}{\sqrt{n\pi}}$ 2- A special case of Jonath
Externí odkaz:
http://arxiv.org/abs/2112.08020
Let alpha = (a,b,...) be a composition. Consider the associated poset F(alpha), called a fence, whose covering relations are x_1 < x_2 < ... < x_{a+1} > x_{a+2} > ... > x_{a+b+1} < x_{a+b+2} < ... . We study the associated distributive lattice L(alph
Externí odkaz:
http://arxiv.org/abs/2008.13232
Publikováno v:
Discrete & Computational Geometry 68, no. 1 (2022), 50-71
The Ehrhart quasipolynomial of a rational polytope $P$ encodes the number of integer lattice points in dilates of $P$, and the $h^*$-polynomial of $P$ is the numerator of the accompanying generating function. We provide two decomposition formulas for
Externí odkaz:
http://arxiv.org/abs/2006.10076
Autor:
Xin, Guoce, Zhong, Yueming
A polynomial $A(q)=\sum_{i=0}^n a_iq^i$ is said to be unimodal if $a_0\le a_1\le \cdots \le a_k\ge a_{k+1} \ge \cdots \ge a_n$. We investigate the unimodality of rational $q$-Catalan polynomials, which is defined to be $C_{m,n}(q)= \frac{1}{[n+m]} \l
Externí odkaz:
http://arxiv.org/abs/1912.01829
The Eulerian distribution on the involutions of the symmetric group is unimodal, as shown by Guo and Zeng. In this paper we prove that the Eulerian distribution on the involutions of the hyperoctahedral group, when viewed as a colored permutation gro
Externí odkaz:
http://arxiv.org/abs/1801.07163
Autor:
Chen, Herman Z. Q., Zhang, Philip B.
We prove the unimodality of the Ehrhart $\delta$-polynomial of the chain polytope of the zig-zag poset, which was conjectured by Kirillov. First, based on a result due to Stanley, we show that this polynomial coincides with the $W$-polynomial for the
Externí odkaz:
http://arxiv.org/abs/1603.08283
A Ringel ladder can be formed by a self-bar-amalgamation operation on a symmetric ladder, that is, by joining the root vertices on its end-rungs. The present authors have previously derived criteria under which linear chains of copies of one or more
Externí odkaz:
http://arxiv.org/abs/1501.06106