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of 22
pro vyhledávání: '"Hlavacek, Max"'
Autor:
Beck, Matthias, Hanada, Mitsuki, Hlavacek, Max, Lentfer, John, Vindas-Meléndez, Andrés R., Waddle, Katie
We study a refinement of the $q,t$-Catalan numbers introduced by Xin and Zhang (2022, 2023) using tools from polyhedral geometry. These refined $q,t$-Catalan numbers depend on a vector of parameters $\vec{k}$ and the classical $q,t$-Catalan numbers a
Externí odkaz:
http://arxiv.org/abs/2407.21226
Autor:
Beck, Matthias, Hlavacek, Max
Stanley introduced in 1986 the order polytope and the chain polytope for a given finite poset. These polytopes contain much information about the poset and have given rise to important examples in polyhedral geometry. In 1993, Reiner introduced signe
Externí odkaz:
http://arxiv.org/abs/2311.04409
Publikováno v:
Advances in Geometry 24 (2024), no. 2, 141-150
The Ehrhart polynomial $\text{ehr}_P(n)$ of a lattice polytope $P$ counts the number of integer points in the $n$-th integral dilate of $P$. The $f^*$-vector of $P$, introduced by Felix Breuer in 2012, is the vector of coefficients of $\text{ehr}_P(n
Externí odkaz:
http://arxiv.org/abs/2210.12271
Autor:
Hlavacek, Max, Solus, Liam
In geometric, algebraic, and topological combinatorics, the unimodality of combinatorial generating polynomials is frequently studied. Unimodality follows when the polynomial is (real) stable, a property often deduced via the theory of interlacing po
Externí odkaz:
http://arxiv.org/abs/2003.07328
Autor:
Hlavacek, Max, Solus, Liam
Publikováno v:
In Journal of Combinatorial Theory, Series A February 2022 186
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Let $n$ points be in crescent configurations in $\mathbb{R}^d$ if they lie in general position in $\mathbb{R}^d$ and determine $n-1$ distinct distances, such that for every $1 \leq i \leq n-1$ there is a distance that occurs exactly $i$ times. Since
Externí odkaz:
http://arxiv.org/abs/1610.07836
Autor:
Burkhardt, Paula, Cohen, Peter, Dewitt, Jonathan, Hlavacek, Max, Miller, Steven J., Sprunger, Carsten, Vu, Yen Nhi Truong, Van Peski, Roger, Yang, Kevin
We introduce a new family of $N\times N$ random real symmetric matrix ensembles, the $k$-checkerboard matrices, whose limiting spectral measure has two components which can be determined explicitly. All but $k$ eigenvalues are in the bulk, and their
Externí odkaz:
http://arxiv.org/abs/1609.03120
Autor:
Cordwell, Katherine, Hlavacek, Max, Huynh, Chi, Miller, Steven J., Peterson, Carsten, Vu, Yen Nhi Truong
Publikováno v:
Res. number theory (2018) 4: 43
Given a recurrence sequence $H$, with $H_n = c_1 H_{n-1} + \dots + c_t H_{n-t}$ where $c_i \in \mathbb{N}_0$ for all $i$ and $c_1, c_t \geq 1$, the generalized Zeckendorf decomposition (gzd) of $m \in \mathbb{N}_0$ is the unique representation of $m$
Externí odkaz:
http://arxiv.org/abs/1608.08764
Publikováno v:
Electron. J. Comb. 23 (3) (2016) #P3.32
There is a well-known bijection between parking functions of a fixed length and maximal chains of the noncrossing partition lattice which we can use to associate to each set of parking functions a poset whose Hasse diagram is the union of the corresp
Externí odkaz:
http://arxiv.org/abs/1602.02175